We consider parameterized verification of systems executing according to the total store ordering (TSO) semantics. The processes manipulate abstract data types over potentially infinite domains. We present a framework that translates the reachability problem for such systems to the reachability problem for register machines enriched with the given abstract data type.

We find the T-duality transformation rules for 2-dimensional (2,1) supersymmetric sigma-models in (2,1) superspace. Our results clarify certain aspects of the (2,1) sigma model geometry relevant to the discussion of T-duality. The complexified duality transformations we find are equivalent to the usual Buscher duality transformations (including an important refinement) together with diffeomorphisms. We use the gauging of sigma-models in (2,1) superspace, which we review and develop, finding a manifestly real and geometric expression for the gauged action. We discuss the obstructions to gauging (2,1) sigma-models, and find that the obstructions to (2,1) T-duality are considerably weaker.

The focus of this thesis is to introduce the path integral and some of its applications. One interpretation of quantum mechanics is that a microscopic system which moves from an initial- to a final state moves through each possible intermediate state. The path integral uses the principle of least action to sum over all such intermediate states to find the evolution of a quantum mechanical system. We compare the path integral approach to that of the Schrödinger equation and show that the two give an equivalent description of quantum mechanics.

To demonstrate the usefulness of the path integral, we introduce low-dimensional quantum field theory (QFT). In particular, we discuss Feynman diagrams. The idea behind Feynman diagrams is to sum over all possible weak interactions between fields to evaluate the properties of a system through the path integral. We also carry out a computation of a low energy effective action in a 0-dimensional model. The result of the computation shows that there is free energy also in a vacuum. Finally, we briefly generalize some of the previous discussion to 1-dimensional QFT. To give an example of a practical application, we give a qualitative discussion of how the path integral can be applied to statistical mechanics to predict the behaviour of superfluids.

Quantum field theories are very good at describing the world around us but use complicated computations that cannot always be solved exactly. Introducing conformal symmetry to quantum field theory can reduce this complexity and allow for quite simple calculation in the best case. This report aims to describe the critical part of the Ising model in 2 dimensions using conformal field theory while assuming only some knowledge of quantum mechanics and complex analysis from the reader. This is done by using the book Conformal Field Theory as the source for information about conformal field theory.

Three-dimensional Chern-Simons vector models display an approximate higher spin symmetry in the large N limit. Their single-trace operators consist of a tower of weakly broken currents, as well as a scalar a of approximate twist 1 or 2. We study the consequences of crossing symmetry for the four-point correlator of a in a 1/N expansion, using analytic bootstrap techniques. To order 1/N we show that crossing symmetry fixes the contribution from the tower of currents, providing an alternative derivation of well-known results by Maldacena and Zhiboedov. When sigma has twist 1 its OPE receives a contribution from the exchange of a itself with an arbitrary coefficient, due to the existence of a marginal sextic coupling. We develop the machinery to determine the corrections to the OPE data of double-trace operators due to this, and to similar exchanges. This in turns allows us to fix completely the correlator up to three known truncated solutions to crossing. We then proceed to study the problem to order 1/N-2. We find that crossing implies the appearance of odd-twist double-trace operators, and calculate their OPE coefficients in a large spin expansion. Also, surprisingly, crossing at order 1/N-2, implies non-trivial O(1/N) anomalous dimensions for even-twist double-trace operators, even though such contributions do not appear in the four-point function at order 1/N (in the case where there is no scalar exchange). We argue that this phenomenon arises due to operator mixing. Finally, we analyse the bosonic vector model with a sextic coupling without gauge interactions, and determine the order 1/N-2 corrections to the dimensions of twist-2 double-trace operators.

eXtended Reality (XR) technologies will play a key role in the digital (r)evolution of modern societies, as they will enable services allowing humans to experience an immersive interaction with virtual, mixed, and augmented realities (VR, MR, and AR) in different societal contexts, including education, entertainment, transportation, manufacturing, and healthcare.

We discuss the geometric origin of discrete higher form symmetries of quantum field theories in terms of defect groups from geometric engineering in M-theory. The flux non-commutativity in M-theory gives rise to (mixed) 't Hooft anomalies for the defect group which constrains the corresponding global structures of the associated quantum fields. We analyze the example of 4d N = 1 SYM gauge theory in four dimensions, and we reproduce the well-known classification of global structures from reading between its lines. We extend this analysis to the case of 7d N = 1 SYM theory, where we recover it from a mixed 't Hooft anomaly among the electric 1-form center symmetry and the magnetic 4-form center symmetry in the defect group. The case of five-dimensional SCFTs from M-theory on toric singularities is discussed in detail. In that context we determine the corresponding 1-form and 2-form defect groups and we explain how to determine the corresponding mixed 't Hooft anomalies from flux non-commutativity. Several predictions for non-conventional 5d SCFTs are obtained. The matching of discrete higher-form symmetries and their anomalies provides an interesting consistency check for 5d dualities.

The repulsive delta-function interaction model in one dimension is reviewed for spinless particles and for spin-1/2 fermions. The problem of solving the differential equation related to the Schrödinger equation is reduced by the Bethe ansatz to a system of algebraic equations. The delta-function interaction is shown to have no effect on spinless fermions which therefore behave like free fermions, in agreement with Pauli's exclusion principle. The ground-state problem of spinless bosons is reduced to an inhomogeneous Fredholm equation of the second kind. In the limit of impenetrable interactions, the spinless bosons are shown to have the energy spectrum of free fermions. The model for spin-1/2 fermions is reduced by the Bethe ansatz to an eigenvalue problem of matrices of the same sizes as the irreducible representations R of the permutation group of N elements. For some R's this eigenvalue problem itself is solved by a generalized Bethe ansatz. The ground-state problem of spin-1/2 fermions is reduced to a generalized Fredholm equation.

This manuscript samples a series of recent results in the quest for a systematic understanding of the space of conformal field theories, with a particular focus on theories with extended supersymmetry. The large majority of results reported here were presented during the second Pollica summer workshop which took place from June 3-21 2019 and focused on mathematical and geometric tools for superconformal field theories. This manuscript represents in many ways a partial summary of the workshop.

We explore and exploit the relation between non-planar correlators in N=4 super-Yang-Mills, and higher-genus closed string amplitudes in type IIB string theory. By conformal field theory techniques we construct the genus-one, four-point string amplitude in AdS5×S5 in the low-energy expansion, dual to an N=4 super-Yang-Mills correlator in the 't Hooft limit at order 1/c2 in a strong coupling expansion. In the flat space limit, this maps onto the genus-one, four-point scattering amplitude for type II closed strings in ten dimensions. Using this approach we reproduce several results obtained via string perturbation theory. We also demonstrate a novel mechanism to fix subleading terms in the flat space limit of AdS amplitudes by using string/M-theory.

We initiate the study of one-loop gluon amplitudes in AdS space. These amplitudes were recently computed at tree level for a variety of backgrounds of the form AdS(d+1) x S-3. For concreteness, we compute the one-loop correction to the massless gluon amplitude on AdS(5) x S-3, which corresponds to the four-point correlator of the flavor current multiplet in the dual 4d N = 2 SCFT. This requires solving a mixing problem that involves tree-level amplitudes of arbitrarily massive Kaluza-Klein modes. The final answer has the same color structure as in flat space but the dependence on Mandelstam variables is more complicated, with logarithms replaced by polygamma functions.

We present a systematic study of N = (2, 2) supersymmetric non-linear sigma models on S-2 with the target being a Kahler manifold. We discuss their reformulation in terms of cohomological field theory. In the cohomological formulation we use a novel version of 2D self-duality which involves a U(1) action on S-2. In addition to the generic model we discuss the theory with target space equivariance corresponding to a supersymmetric sigmamodel coupled to a non-dynamical supersymmetric background gauge multiplet. We discuss the localization locus and perform a one-loop calculation around the constant maps. We argue that the theory can be reduced to some exotic model over the moduli space of holomorphic disks.

We construct a new Yang-Mills Lagrangian based on a notion of minimal coupling that incorporates classical spin effects. The construction relies on the introduction of a new covariant derivative, which we name “classical spin covariant derivative”, that is compatible with the three-point interaction of the √‾‾‾Kerr solution with the gauge field. The resulting Lagrangian, besides the correct three-point coupling, predicts a unique choice for contact terms and therefore it can be used to compute higher-point amplitudes such as the Compton, unaffected by spurious poles. Using double copy techniques we use this theory to extract gravity amplitudes and observables that are relevant to describe Kerr binary dynamics to all orders in the spin. In particular, we compute the 2PM (O(G²_N)) 2 → 2 elastic scattering amplitude between two classically spinning objects to all orders in the spin and use it to extract the 2PM scattering angle.

Infrared effects in the scattering of particles in gravity and electrodynamics entail an exchange of relativistic angular momentum between pairs of particles and the gauge field. Due to this exchange particles can carry an asymptotically non-vanishing "pairwise" boost-like angular momentum proportional to the product of their couplings to the field. At the quantum level this asymptotic angular momentum suggests the existence of a new quantum number carried by multi-particle states. We argue that such quantum number is related to a modification of the action of the generators of Lorentz transformations on multi-particle states. We derive such a modification using a group-theoretic argument based on the little group of the conformal primary basis for asymptotic states. The corresponding representation is an extension of the ordinary multi-particle Fock representation of the Poincar & eacute; group. The new multi-particle states belonging to such representation no longer factorize into tensor products of one-particle states. Viewed from a gravitational point of view, our results provide evidence for a universal breakdown of the description of multi-particle sates in terms of tensor products of one-particle states due to infrared back-reaction.

We introduce a classical version of the loop corrected soft graviton theorem and we use it to compute the universal part of the one-loop (2PM) waveform up to sub-subleading order in the energy ω of the emitted graviton for spinless black holes scattering. In particular, we compute the action of the soft operators on the classically resummed four-point amplitude, that can be written in terms of the exponential of the eikonal phase (and is therefore non-perturbative in the Newton's constant ) and then we perform the usual Post-Minkowskian expansion in powers of . We find perfect agreement with the existing 2PM literature at the orders ω⁻¹, logω and ωlog²ω, which are universal. Furthermore, we use this method to compute the universal part of the ωlogω contribution to the 2PM waveform. Even if in the present analysis we limit ourselves to compute the soft 2PM waveform, our general formulae can be used to extract all universal PM orders of the terms connected with the infrared divergences up to non-linear memory contributions, once the impulse at the corresponding precision is known. Our approach, based on the resummed eikonal amplitude, gives a unified picture of the various computations of the classical soft graviton behaviour that are present in the literature since the seminal paper by Weinberg (1965 Phys. Rev. 140 B516–24).

Using universal predictions provided by classical soft theorems, we revisit the energy emission spectrum for gravitational scatterings of compact objects in the low-frequency expansion. We calculate this observable beyond the zero-frequency limit, retaining an exact dependence on the kinematics of the massive objects. This allows us to study independently the ultrarelativistic or massless limit, where we find agreement with the literature, and the small-deflection or post-Minkowskian (PM) limit, where we provide explicit results up to O\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{O} $$\end{document}(G5). These confirm that the high-velocity limit of a given PM order is smoothly connected to the corresponding massless result whenever the latter is analytic in the Newton constant G. We also provide explicit expressions for the waveforms to order omega-1, log omega, omega(log omega)2 in the soft limit, omega -> 0, expanded up to sub-subleading PM order, as well as a conjecture for the logarithmic soft terms of the type omega n-1(log omega)n with n >= 3.

We study the rigid limit of a class of hypermultiplet moduli spaces appearing in Calabi-Yau compactifications of type IIB string theory, which is induced by a local limit of the Calabi-Yau. We show that the resulting hyperkahler manifold is obtained by performing a hyperkahler quotient of the Swann bundle over the moduli space, along the isometries arising in the limit. Physically, this manifold appears as the target space of the non-linear sigma model obtained by compactification of a five-dimensional gauge theory on a torus. This allows to compute dyonic and stringy instantons of the gauge theory from the known results on D-instantons in string theory. Besides, we formulate a simple condition on the existence of a non-trivial local limit in terms of intersection numbers of the Calabi-Yau, and find an explicit form for the hypermultiplet metric including corrections from all mutually non-local D-instantons, which can be of independent interest.

Electron energy-loss magnetic chiral dichroism (EMCD) has the potential to measure magnetic properties of the materials at atomic resolution but the complex distribution of magnetic signals in the zone axis and the overlapping diffraction discs at higher beam convergence angles make the EMCD signal acquisition challenging. Recently, the use of ventilator apertures to acquire the EMCD signals with atomic resolution was proposed. Here we give the experimental demonstration of several types of ventilator apertures and obtain a clear EMCD signal at beam semiconvergence angles of 5 mrad. To simplify the experimental procedures, we propose a modified ventilator aperture which not only simplifies the complex scattering conditions but reduces the influence of lens aberrations on the EMCD signal as compared to the originally proposed ventilator apertures. In addition, this modified aperture can be used to analyze magnetic crystals with various symmetries and we demonstrate this feature by acquiring EMCD signals on different zone axis orientations of an Fe crystal. With the same aperture we obtain EMCD signals with convergence angles corresponding to atomic resolution electron probes. After the theoretical demonstration of the EMCD signal on a zone axis orientation at high beam convergence angles, this work thus overcomes the experimental and methodological hurdles and enables atomic resolution EMCD on the zone axis by using apertures.

Equivariant localisation is based on exploiting certain symmetries of some systems, generally represented by a non-free action of a Lie group on a manifold, to reduce the dimensionality of integral calculations that commonly appear in theoretical physics. In this work we present Cartan's model of equivariant cohomology in different scenarios, such as differential manifolds, symplectic manifolds or vector bundles and we reproduce the main corresponding localisation results.

We obtain the brane setup describing 3d N = 2 dualities for USp(2N(c)) and U(Nc) SQCD with monopole superpotentials. This classification follows from a complete analysis of affine and twisted affine compactifications from 4d. The analysis leads to a new duality for the unitary case that has previously been overlooked in the literature. We check this by matching the three-sphere partition function of the two sides of this new duality and find a perfect agreement. Furthermore, we use the partition function to predict new 3d N = 2 dualities for SQCD with monopole superpotentials and tensorial matter.

We study heterotic Calabi-Yau models with hypercharge flux breaking, where the visible E-8 gauge group is directly broken to the standard model group by a nonflat gauge bundle, rather than by a two-step process involving an intermediate grand unified theory and a Wilson line. It is shown that the required alternative E-8 embeddings of hypercharge, normalized as required for gauge unification, can be found and we classify these possibilities. However, for all but one of these embeddings we prove a general no-go theorem which asserts that no suitable geometry and vector bundle leading to a standard model spectrum can be found. Intuitively, this happens due to the large number of index conditions which have to be imposed in order to obtain a correct physical spectrum in the absence of an underlying grand unified theory.

In this work, we study F-theory compactifications on manifolds. Such geometries, which we study in both 4- and 6dimensions, are both ubiquitous within the set of Calabi-Yau manifolds and play a crucial role in heterotic/F-theory duality. We discuss the most general formulation of P1-bundles of this type, as well as fibrations which degenerate at higher codimension loci. In the course of this study, we find a number of new phenomena. For example, in both 4- and 6-dimensions we find transitions whereby the base of a P1-bundle can change nature, or "jump ", at certain loci in complex structure moduli space. We discuss the implications of this jumping for the associated heterotic duals. We argue that P1-bundles with only rational sections lead to heterotic duals where the Calabi-Yau manifold is elliptically fibered over the section of the P1 bundle, and not its base. As expected, we see that degenerations of the P1 fibration of the F-theory base correspond to 5-branes in the dual heterotic physics, with the exception of cases in which the fiber degenerations exhibit monodromy. Along the way, we discuss a set of useful formulae and tools for describing F-theory compactifications on this class of Calabi-Yau manifolds.

Heterotic compactifications on Calabi-Yau threefolds frequently exhibit textures of vanishing Yukawa couplings in their low energy description. The vanishing of these couplings is often not enforced by any obvious symmetry and appears to be topological in nature. Recent results used differential geometric methods to explain the origin of some of this structure [1, 2]. A vanishing theorem was given which showed that the effect could be attributed, in part, to the embedding of the Calabi-Yau manifolds of interest inside higher dimensional ambient spaces, if the gauge bundles involved descended from vector bundles on those larger manifolds. In this paper, we utilize an algebro-geometric approach to provide an alternative derivation of some of these results, and are thus able to generalize them to a much wider arena than has been considered before. For example, we consider cases where the vector bundles of interest do not descend from bundles on the ambient space. In such a manner we are able to highlight the ubiquity with which textures of vanishing Yukawa couplings can be expected to arise in heterotic compactifications, with multiple different constraints arising from a plethora of different geometric features associated to the gauge bundle.

When mass-deformed ABJM theory is considered on S-3, the partition function of the theory localises, and is given by a matrix model. At large N, we solve this model in the decompactification limit, where the radius of the three-sphere is taken to infinity. In this limit, the theory exhibits a rich phase structure with an infinite number of third-order quantum phase transitions, accumulating at strong coupling.

A review of Boundary and defect conformal field theory: open problems and applications, following a workshop held at Chicheley Hall, Buckinghamshire, UK, 7-8 Sept. 2017. We attempt to provide a broad, bird's-eye view of the latest progress in boundary and defect conformal field theory in various sub-fields of theoretical physics, including the renormalization group, integrability, conformal bootstrap, topological field theory, supersymmetry, holographic duality, and more. We also discuss open questions and promising research directions in each of these sub-fields, and combinations thereof.

The coupling of electrons to spin excitations and the generation of magnons is essential for spin mixing in the ultrafast magnetization dynamics of 3d ferromagnets. Although magnon energies are generally much larger than phonon energies, until now their electronic band renormalization effect in 3d ferromagnets suggests a significantly weaker quasiparticle interaction. Using spin- and angle-resolved photoemission, we show an extraordinarily strong renormalization leading to two-branch splitting of an iron surface resonance at ~& nbsp;200 meV. Its strong magnetic linear dichroism unveils the magnetic nature and momentum dependence of the energy renormalization. By determining the frequency- and momentum-dependent self-energy due to generic electron-boson interaction to compute the resultant electron spectral function, we suggest that the surface-state splitting can be described by strong coupling to an optical spin wave in an iron thin film.& nbsp;& nbsp;Published under an exclusive license by AIP Publishing.

We conjecture explicit evolution formulas for Khovanov polynomials, which for any particular knot are Laurent polynomials of complex variables q and T, for pretzel knots of genus g in some regions in the space of winding parameters n0,,ng. Our description is exhaustive for genera 1 and 2. As previously observed Anokhina and Morozov (2018), Dunin-Barkowski et al. (2019), evolution at T not equal -1 is not fully smooth: it switches abruptly at the boundaries between different regions. We reveal that this happens also at the boundary between thin and thick knots, moreover, the thick-knot domain is further stratified. For thin knots the two eigenvalues 1 and lambda =q2T, governing the evolution, are the standard T-deformation of the eigenvalues of the R-matrix 1 and -q2. However, in thick knots' regions extra eigenvalues emerge, and they are powers of the "naive" lambda, namely, they are equal to lambda 2,,lambda g. From point of view of frequencies, i.e. logarithms of eigenvalues, this is frequency doubling (more precisely, frequency multiplication) - a phenomenon typical for non-linear dynamics. Hence, our observation can signal a hidden non-linearity of superpolynomial evolution. To give this newly observed evolution a short name, note that when lambda is pure phase the contributions of lambda 2,,lambda g oscillate "faster" than the one of lambda. Hence, we call this type of evolution "nimble".

We derive an optical theorem for perturbative CFTs which computes the double discontinuity of conformal correlators from the single discontinuities of lower order correlators, in analogy with the optical theorem for flat space scattering amplitudes. The theorem takes a purely multiplicative form in the CFT impact parameter representation used to describe high-energy scattering in the dual AdS theory. We use this result to study four-point correlation functions that are dominated in the Regge limit by the exchange of the graviton Regge trajectory (Pomeron) in the dual theory. At one-loop the scattering is dominated by double Pomeron exchange and receives contributions from tidal excitations of the scattering states which are efficiently described by an AdS vertex function, in close analogy with the known Regge limit result for one-loop string scattering in flat space at finite string tension. We compare the flat space limit of the conformal correlator to the flat space results and thus derive constraints on the one-loop vertex function for type IIB strings in AdS and also on general spinning tree level type IIB amplitudes in AdS.

Starting with on-shell amplitudes compatible with the scattering of Kerr black holes up to Comptonamplitude contact terms, we produce the gravitational waveform and memory effect including spin at their leading post-Minkowskian orders to all orders in the spins of both scattering objects. For the memory effect, we present results at next-to-leading order as well, finding a closed form for all spin orders when the spins are anti-aligned and equal in magnitude. Considering instead generically oriented spins, we produce the next-to-leading-order memory to sixth order in spin. Compton-amplitude contact terms up to sixth order in spin are included throughout our analysis.

We calculate the scattering amplitude of two rotating objects with the linear-in-curvature spin-induced multipoles of Kerr black holes at O(G²) and all orders in the spins of both objects. This is done including the complete set of contact terms potentially relevant to Kerr-black-hole scattering at O(G²). As such, Kerr black holes should be described by this scattering amplitude for a specific choice of values for the contact-term coefficients. The inclusion of all potential contact terms means this amplitude allows for a comprehensive search for structures emerging for certain values of the coefficients, and hence special properties that might be exhibited by Kerr-black-hole scattering. Our result can also act as a template for comparison for future computations of classical gravitational high-spin scattering.

Making use of the recently derived, all-spin, opposite-helicity Compton amplitude, we calculate the classical gravitational scattering amplitude for one spinning and one spinless object at O(G(2)) and all orders in spin. By construction, this amplitude exhibits the spin structure that has been conjectured to describe Kerr black holes. This spin structure alone is not enough to fix all deformations of the Compton amplitude by contact terms, but when combined with considerations of the ultrarelativistic limit we can uniquely assign values to the parameters remaining in the even-in-spin sector. Once these parameters are determined, much of the spin dependence of the amplitude resums into hypergeometric functions. Finally, we derive the eikonal phase for aligned-angular-momentum scattering.

The classical scattering of spinning objects is well described by the spinor-helicity formalism for heavy particles. Using these variables, we derive spurious-pole-free, all-spin opposite-helicity Compton amplitudes (factorizing on physical poles to the minimal, all-spin three-point amplitudes) in the classical limit for QED, QCD, and gravity. The cured amplitudes are subject to deformations by contact terms, the vast majority of whose contributions we can fix by imposing a relation between spin structures - motivated by lower spin multipoles of black hole scattering - at the second post-Minkowskian (2PM) order. For QED and gravity, this leaves a modest number of unfixed coefficients parametrizing contact-term deformations, while the QCD amplitude is uniquely determined. Our gravitational Compton amplitude allows us to push the state-of-the-art of spinning-2PM scattering to any order in the spin vectors of both objects; we present results here and in the supplementary material file 2PMSpin8Aux.nb up to eighth order in the spin vectors. Interestingly, despite leftover coefficients in the Compton amplitude, imposing the aforementioned relation between spin structures uniquely fixes some higher-spin parts of the 2PM amplitude.

We propose a stringy construction giving rise to a class of interacting and non-supersymmetric CFT's in six dimensions. Such theories may be obtained as an IR conformal fixed point of an RG flow ending up in a (1,0)" role="presentation" style="display: inline; font-size: 13.6px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; font-family: arial, verdana, sans-serif; position: relative;">(1,0)(1,0) theory in the UV. We provide the due holographic evidence in the context of massive type IIA on AdS7×M3" role="presentation" style="display: inline; font-size: 13.6px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; font-family: arial, verdana, sans-serif; position: relative;">AdS7×M3AdS7×M3, where M3" role="presentation" style="display: inline; font-size: 13.6px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; font-family: arial, verdana, sans-serif; position: relative;">M3M3 is topologically an S3" role="presentation" style="display: inline; font-size: 13.6px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; font-family: arial, verdana, sans-serif; position: relative;">S3S3. In particular, in this paper we present a 10d flow solution which may be interpreted as a non-BPS bound state of NS5, D6 and D6¯" role="presentation" style="display: inline; font-size: 13.6px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; font-family: arial, verdana, sans-serif; position: relative;">D6⎯⎯⎯⎯⎯⎯⎯D6¯ branes. Moreover, by adopting its 7d effective desciption, we are able to holographically compute the free energy and the operator spectrum in the novel IR conformal fixed point.

One of the hallmarks of 6D superconformal field theories (SCFTs) is that on a partial tensor branch, all known theories resemble quiver gauge theories with links comprised of 6D conformal matter, a generalization of weakly coupled hypermultiplets. In this paper we construct 4D quiverlike gauge theories in which the links are obtained from compactifications of 6D conformal matter on Riemann surfaces with flavor symmetry fluxes. This includes generalizations of super QCD with exceptional gauge groups and quarks replaced by 4D conformal matter. Just as in super QCD, we find evidence for a conformal window as well as confining gauge group factors depending on the total amount of matter. We also present F-theory realizations of these field theories via elliptically fibered Calabi-Yau fourfolds. Gauge groups (and flavor symmetries) come from 7-branes wrapped on surfaces, conformal matter localizes at the intersection of pairs of 7-branes, and Yukawas between 4D conformal matter localize at points coming from triple intersections of 7-branes. Quantum corrections can also modify the classical moduli space of the F-theory model, matching expectations from effective field theory.

Choi, Kim, Kim, and Nahmgoong have recently pioneered analyzing a Cardy-like limit of the superconformal index of the 4d N=4 theory with complexified fugacities which encodes the entropy of the dual supersymmetric AdS(5) blackholes. Here we study the Cardy-like asymptotics of the index within the rigorous framework of elliptic hypergeometric integrals, thereby filling a gap in their derivation of the blackhole entropy function, finding a new blackhole saddle-point, and demonstrating novel bifurcation phenomena in the asymptotics of the index as a function of fugacity phases. We also comment on the relevance of the supersymmetric Casimir energy to the blackhole entropy function in the present context.

We revisit the vacuum structure of the N = 1 Intriligator-Seiberg-Shenker model on R-3 x S-1. Guided by the Cardy-like asymptotics of its Romelsberger index, and building on earlier semi-classical results by Poppitz and Unsal, we argue that previously overlooked non-perturbative effects generate a Higgs-type potential on the classical Coulomb branch of the low-energy effective 3d N = 2 theory. In particular, on part of the Coulomb branch we encounter the first instance of a dynamically-generated quintic monopole superpotential.

We study the Cardy-like asymptotics of the 4d N = 4 index and demonstrate the existence of partially deconfined phases where the asymptotic growth of the index is not as rapid as in the fully deconfined case. We then take the large-N limit after the Cardy-like limit and make a conjecture for the leading asymptotics of the index. While the Cardy-like behavior is derived using the integral representation of the index, we demonstrate how the same results can be obtained using the Bethe ansatz type approach as well. In doing so, we discover new non-standard solutions to the elliptic Bethe ansatz equations including continuous families of solutions for SU(N ) theory with N >= 3. We argue that the existence of both standard and continuous non-standard solutions has a natural interpretation in terms of vacua of N = 1 theory on (3)x S-1.

We study the Casimir energy of bulk fields in AdS3 and its relation to subleading terms in the central charge of the dual CFT2. Computing both sides of the standard CFT2 relation E=−c/12 independently we show that this relation is not necessarily satisfied at the level of individual bulk supergravity states, but in theories with sufficient supersymmetry it is restored at the level of bulk supermultiplets. Assuming only (0,2) supersymmetry (or more), we improve the situation by relating quantum corrections to the central charge and the supersymmetric Casimir energy which in turn is related to an index. These relations adapt recent progress on the AdS5/CFT4 correspondence to AdS3/CFT2 holography. We test our formula successfully in several examples, including the (0,4) MSW theory describing classes of 4D black holes and the large (4,4) theory that is interesting for higher spin holography. We also make predictions for the subleading central charges in several recently proposed (2,2) dualities where the CFT2 is not yet well-understood.

This master thesis is framed in the striking correspondence between gravity theories in Anti-de Sitter spacetime (AdS) and Conformal Field Theories (CFT). This is usually known as AdS/CFT duality and relates gravity theories in the bulk with CFTs that live in their conformal boundary. We start by presenting the notion of CFTs and some of the results and techniques that are widely used in this field. This includes conformal correlators for scalar and spin operators, the state-operator correspondence and the operator product expansion (OPE) of operators. The embedding formalism and the index-free notation to encode tensors in polynomials are also discussed and used throughout this work. The basic notions of AdS are outlined and CFT at finite temperature is then introduced. We include a review of thermal blocks and thermal coefficients for a thermal two-point function between scalar fields in mean field theory. We then analyse the thermal two-point function for conserved currents, which was not known in the literature. Finally, we start a study of its thermal blocks and thermal coefficients for the mean field theory application.

In this work we establish that the Inozemtsev system is the Seiberg-Witten integrable system encoding the Coulomb branch physics of 4d N = 2 USp(2N) gauge theory with four fundamental and (for N >= 2) one antisymmetric tensor hypermultiplets. We describe the transformation from the spectral curves and canonical one-forms of the Inozemtsev system in the N = 1 and N = 2 cases to the Seiberg-Witten curves and differentials explicitly, along with the explicit matching of the modulus of the elliptic curve of spectral parameters to the gauge coupling of the field theory, and of the couplings of the Inozemtsev system to the field theory mass parameters. This result is a particular instance of a more general correspondence between crystallographic elliptic Calogero-Moser systems with Seiberg-Witten integrable systems, which will be explored in future work.

We reexamine the vacuum structure of three-dimensional quantum chromodynamics (QCD₃) with gauge group SU(N), N_f fundamental quark flavors, and a level-k Chern-Simons term. This analysis can be reliably carried out in the large-N, fixed N_f, k limit of the theory, up to certain assumptions that we spell out explicitly. At leading order in the large-N expansion we find N_f + 1 distinct, exactly degenerate vacuum superselection sectors with different patterns of flavor-symmetry breaking. The associated massless Nambu-Goldstone bosons are generically accompanied by topological Chern-Simons theories. This set of vacua explicitly realizes many candidate phases previously proposed for QCD₃. At subleading order in the large-N expansion, the exact degeneracy between the different superselection sectors is lifted, leading to a multitude of metastable vacua. If we dial the quark masses, different metastable vacua can become the true vacuum of the theory, leading to a sequence of first-order phase transitions. We show that this intricate large-N dynamics can be captured by the previously proposed bosonic dual theories for QCD₃, provided these bosonic duals are furnished with a suitable scalar potential. Interestingly, this potential must include terms beyond quartic order in the scalar fields.

The phenomenon of BCJ duality implies that gauge theories possess an abstract kinematic algebra, mirroring the non-abelian Lie algebra underlying the colour information. Although the nature of the kinematic algebra is known in certain cases, a full understanding is missing for arbitrary non-abelian gauge theories, such that one typically works outwards from well-known examples. In this paper, we pursue an orthogonal approach, and argue that simpler abelian gauge theories can be used as a testing ground for clarifying our understanding of kinematic algebras. We first describe how classes of abelian gauge fields are associated with well-defined subalgebras of the diffeomorphism algebra. By considering certain special subalgebras, we show that one may construct interacting theories, whose kinematic algebras are inherited from those already appearing in a related abelian theory. Known properties of (anti-)self-dual Yang-Mills theory arise in this way, but so do new generalisations, including self-dual electromagnetism coupled to scalar matter. Furthermore, a recently obtained non-abelian generalisation of the Navier-Stokes equation fits into a similar scheme, as does Chern-Simons theory. Our results provide useful input to further conceptual studies of kinematic algebras.

In double-field inflation, which exploits two scalar fields, one of the fields rolls slowly during inflation whereas the other field is trapped in a meta-stable vacuum. The nucleation rate from the false vacuum to the true one becomes substantial enough that triggers a first order phase transition and ends inflation. We revisit the question of first order phase transition in an "extended" model of hybrid inflation, realizing the double-field inflationary scenario, and correctly identify the parameter space that leads to a first order phase transition at the end of inflation. We compute the gravitational wave profile which is generated during this first order phase transition. Assuming instant reheating, the peak frequency falls in the 1 GHz to 10 GHz frequency band and the amplitude varies in the range 10(-11) less than or similar to Omega(GW)h(2) <= 10(-8), depending on the value of the cosmological constant in the false vacuum. For a narrow band of vacuum energies, the first order phase transition can happen after the end of inflation via the violation of slow-roll, with a peak frequency that varies from 1 THz to 100 THz. For smaller values of cosmological constant, even though inflation can end via slow-roll violation, the universe gets trapped in a false vacuum whose energy drives a second phase of eternal inflation. This range of vacuum energies do not lead to viable inflationary models, unless the value of the cosmological constant is compatible with the observed value, M similar to 10(-3) eV.

We investigate the effect of non-linear dispersion relations on the bispectrum. In particular, we study the case were the modified relations do not violate the WKB condition at early times, focusing on a particular example which is exactly solvable: the Jacobson-Corley dispersion relation with quartic correction with positive coefficient to the squared linear relation. We find that the corrections to the standard result for the bispectrum are suppressed by a factor H-2/p(c)(2) where p(c) is the scale where the modification to the dispersion relation becomes relevant. The modification is mildly configuration-dependent and equilateral configurations are more suppressed with respect to the local ones, by a factor of one percent. There is no configuration leading to enhancements. We then analyze the results in the framework of particle creation using the approximate gluing method of Brandenberger and Martin, which relates more directly to the modeling of the trans-Planckian physics via modifications of the vacuum at a certain cutoff scale. We show that the gluing method overestimates the leading order correction to the spectrum and bispectrum by one and two orders, respectively, in We discuss the various approximation and conclude that for dispersion relations not violating WKB at early times the particle creation is small and does not lead to enhanced contributions to the bispectrum. We also show that in many cases enhancements do not our when modeling the trans-Planckian physics via modifications of the vacuum at a certain cutoff scale. Most notably they are only of order O(1) when the Bogolyubov coefficients accounting for particle creation are determined by the Wronskian condition and the minimization of the uncertainty between the field and its conjugate momentum.

We observe that the dominant one loop contribution to the graviton propagator in the theory of N (N >> 1) light scalar fields phi(a) (with masses smaller than M-pI/root N) minimally coupled to Einstein gravity is proportional to N while that of graviton-scalar-scalar interaction vertex is N independent. We use this to argue that the coefficient of the R phi(2)(a) term appearing at one loop level is 1/N suppressed. This observation provides a resolution to the quantum eta-problem, that the slow-roll parameter eta receives order one quantum loop corrections for inflationary models built within the framework of scalar fields minimally coupled to Einstein gravity, for models involving large number of fields. As particular examples, we employ this to argue in favor of the absence of eta-problem in multi-field inflationary scenarios of M-flation and N-flation.

Motivated by the dynamics of N coincident D3 branes in some specific flux compactifications, we construct an inflationary model in which inflation is driven by three N Oe N hermitian matrices i,i = 1,2, 3, hence the name Matrix Inflation, or M-f lation for short. We show that one can consistently restrict the classical dynamics to a sector in which the i are proportional to the N Oe N irreducible representation of SU(2). In this sector our model behaves like an effective inflaton field, which t akes super-Planckian field values, and 3N(2) -' 1 isocurvature fields. These may have the observational effects such as production of iso-curvature perturbations on cosmic microwave background. Moreover, the existence of these extra scalars provides us wi th a natural preheating mechanism and exit from inflation. Due to the super-Planckian excursions of the canonical effective inflaton, the model is capable of producing a considerable amount of gravity waves that can be probed by future CMB polarization ex periments. Furthermore, the fine-tunings associated with unnaturally small couplings in the chaotic type inflationary scenarios are removed. We also show that even if the cutoff of the theory is lowered by the square of number of species, one can still us e the effective field theory approach to justify the absence of higher dimensional operators.

In this paper we study gauged M-flation. an inflationary model in which inflation is driven by three N x N scalar field matrices in the adjoint representation of U(N) gauge group. We focus our study on the gauged M-flation model which could be derived front the dynamics of a stack of D3-branes in appropriate background flux. The background inflationary dynamics is unaltered compared to the ungauged case of [1], while the spectrum of "spectator species", the isocurvature modes, differs from the ungauged case. Presence of a large number of spectators, although irrelevant to the slow-roll inflationary dynamics, has been argued to lower the effective UV cutoff Lambda of the theory from the Planck mass M-pl, putting into question the main advantage of M-flation in not having super-Planckian field values and unnaturally small couplings. Through a careful analysis of the spectrum of the spectators we argue that contrary to what happens in N-flation models, M-flation is still UV safe with the modified (reduced) effective UV cutoff Lambda, which we show to be of order (0.5 - 1) x 10(-1)M(pl). Moreover, we argue that the string scale in our gauged M-flation model is larger than Lambda by a factor of 10 and hence one can also neglect stringy effects. We also comment on the stability of classical inflationary paths in the gauged M-flation.

We identify a two-parameter family of excited states within slow-roll inflation for which either the corrections to the two-point function or the characteristic signatures of excited states in the three-point function - i.e. the enhancement for the flattened momenta configurations- are absent. These excited states may nonetheless violate the adiabaticity condition maximally. We dub these initial states of inflation calm excited states. We show that these two sets do not intersect, i.e., those that leave the power-spectrum invariant can be distinguished from their bispectra, and vice versa. The same set of calm excited states that leave the two-point function invariant for slow-roll inflation, do the same task for DBI inflation. However, at the level of three-point function, the calm excited states whose flattened configuration signature is absent for slow-roll inflation, will lead to an enhancement for DBI inflation generally, although the signature is smaller than what suggested by earlier analysis. This example also illustrates that imposing the Wronskian condition is important for obtaining a correct estimate of the non-Gaussian signatures.

We consider D-dimensional amplitudes in R-2 gravities (conformal gravity in D = 4) and in the recently introduced (DF)(2) gauge theory, from the perspective of the CHY formulae and ambitwistor string theory. These theories are related through the BCJ double-copy construction, and the (DF)(2) gauge theory obeys color-kinematics duality. We work out the worldsheet details of these theories and show that they admit a formulation as integrals on the support of the scattering equations, or alternatively, as ambitwistor string theories. For gravity, this generalizes the work done by Berkovits and Witten on conformal gravity to D dimensions. The ambitwistor is also interpreted as a D-dimensional generalization of Witten's twistor string (SYM + conformal supergravity). As part of our ambitwistor investigation, we discover another (DF)(2) gauge theory containing a photon that couples to Einstein gravity. This theory can provide an alternative KLT description of Einstein gravity compared to the usual Yang-Mills squared.

In this work we investigate the classical constraints imposed on the supergravity and super Yang-Mills backgrounds in the alpha' -> 0 limit of the heterotic string using the pure spinor formalism. Guided by the recently observed sectorization of the model, we show that all the ten-dimensional constraints are elegantly obtained from the single condition of nilpotency of the BRST charge.