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Scattering Amplitudes in Supersymmetric Quantum Chromodynamics and Gravity
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.ORCID iD: 0000-0002-6697-775x
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Quantum field theory is a theoretical framework for the description of nature in terms of fundamental particles, fields and their interactions. In the quantum regime, elementary scattering processes are observables in many experiments and studied in theoretical physics. The theoretical understanding of scattering amplitudes is often based on a perturbative analysis in powers of the coupling strength of the fundamental forces. Whereas the computation of scattering amplitudes has been dominated by Feynman diagram constructions for a long time, new methods have lead to a multitude of novel results in the last 20-30 years. Thereafter discoveries of new representations, dualities and construction methods have enormously increased our understanding of the mathematical structure of scattering amplitudes.

In this thesis we focus on a particular structure of gauge theory amplitudes known as the color-kinematics duality. Closely tied to this duality is the double copy construction of gravitational amplitudes, and a set of identities among basic building blocks of the gauge theory, the BCJ identities. Using methods developed for the study of this duality, we obtain new results for scattering amplitudes in non-maximal supersymmetric Yang-Mills coupled to massless fundamental matter at one and two loops. We immediately construct amplitudes in supergravity theories via the double copy. Furthermore, we include methods and results for the integration of gauge theory amplitudes and the ultraviolet structure of supergravity amplitudes.

In a second part we present ideas related to the identification of basic building blocks that underlie the construction of  scattering amplitudes. A decomposition of gauge theory amplitudes into color- and kinematic-dependent contributions exposes a set of primitive objects. Relations among these objects allow us to identify a minimal set of independent kinematic building blocks.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2019. , p. 107
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1806
Keywords [en]
Scattering Amplitudes, Supersymmetric Gauge Theory, Supergravity, Quantum Chromodynamics
National Category
Subatomic Physics
Research subject
Physics and Astronomy specializing in Theoretical Physics
Identifiers
URN: urn:nbn:se:uu:diva-381772ISBN: 978-91-513-0652-0 (print)OAI: oai:DiVA.org:uu-381772DiVA, id: diva2:1305181
Public defence
2019-06-10, Häggsalen, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, 13:15 (English)
Opponent
Supervisors
Available from: 2019-05-17 Created: 2019-04-16 Last updated: 2019-06-17
List of papers
1. Two-loop supersymmetric QCD and half-maximal supergravity amplitudes
Open this publication in new window or tab >>Two-loop supersymmetric QCD and half-maximal supergravity amplitudes
2017 (English)In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, no 9, article id 019Article in journal (Refereed) Published
Abstract [en]

Using the duality between color and kinematics, we construct two-loop four point scattering amplitudes in N = 2 super-Yang-Mills (SYM) theory coupled to N-f fundamental hypermultiplets. Our results are valid in D <= 6 dimensions, where the upper bound corresponds to six-dimensional chiral N = (1, 0) SYM theory. By exploiting a close connection with N = 4 SYM theory-and, equivalently, six-dimensional N = (1, 1) SYM theory we find compact integrands with four-dimensional external vectors in both the maximally-helicity-violating (MHV) and all-chiral-vector sectors. Via the double-copy construction corresponding D-dimensional half-maximal supergravity amplitudes with external graviton multiplets are obtained in the MHV and all-chiral sectors. Appropriately tuning N-f enables us to consider both pure and matter-coupled supergravity, with arbitrary numbers of vector multiplets in D = 4. As a bonus, we obtain the integrands of the genuinely six-dimensional supergravities with N = (1, 1) and N = (2, 0) supersymmetry. Finally, we extract the potential ultraviolet divergence of half-maximal supergravity in D = 5-2 is an element of and show that it non-trivially cancels out as expected.

Keywords
Scattering Amplitudes, Supergravity Models, Supersymmetric Gauge Theory, Gauge Symmetry
National Category
Physical Sciences
Identifiers
urn:nbn:se:uu:diva-335854 (URN)10.1007/JHEP09(2017)019 (DOI)000411022400006 ()
Funder
Swedish Research Council, 621-2014-5722Knut and Alice Wallenberg Foundation, KAW 2013.0235
Available from: 2018-01-22 Created: 2018-01-22 Last updated: 2019-04-16Bibliographically approved
2. Cyclic Mario worlds - color-decomposition for one-loop QCD
Open this publication in new window or tab >>Cyclic Mario worlds - color-decomposition for one-loop QCD
2018 (English)In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, no 4, article id 141Article in journal (Refereed) Published
Abstract [en]

We present a new color decomposition for QCD amplitudes at one-loop level as a generalization of the Del Duca-Dixon-Maltoni and Johansson-Ochirov decomposition at tree level. Starting from a minimal basis of planar primitive amplitudes we write down a color decomposition that is free of linear dependencies among appearing primitive amplitudes or color factors. The conjectured decomposition applies to any number of quark flavors and is independent of the choice of gauge group and matter representation. The results also hold for higher-dimensional or supersymmetric extensions of QCD. We provide expressions for any number of external quark-antiquark pairs and gluons. [GRAPHICS] .

Keywords
Perturbative QCD, Scattering Amplitudes, Gauge Symmetry
National Category
Subatomic Physics
Identifiers
urn:nbn:se:uu:diva-355467 (URN)10.1007/JHEP04(2018)141 (DOI)000432044000001 ()
Funder
Swedish Research Council, 621-2014-5722Knut and Alice Wallenberg Foundation, KAW 2013.0235
Available from: 2018-06-29 Created: 2018-06-29 Last updated: 2019-04-16Bibliographically approved
3. Two-loop N=2 SQCD amplitudes with external matter from iterated cuts
Open this publication in new window or tab >>Two-loop N=2 SQCD amplitudes with external matter from iterated cuts
2019 (English)In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, no 7, article id 120Article in journal (Refereed) Published
Abstract [en]

We develop an iterative method for constructing four-dimensional generalized unitarity cuts in N = 2 supersymmetric Yang-Mills (SYM) theory coupled to fundamental matter hypermultiplets (N = 2 SQCD). For iterated two-particle cuts, specifically those involving only four-point amplitudes, this implies simple diagrammatic rules for assembling the cuts to any loop order, reminiscent of the rung rule in N = 4 SYM. By identifying physical poles, the construction simplifies the task of extracting complete integrands. In combination with the duality between color and kinematics we construct all four-point massless MHV-sector scattering amplitudes up to two loops in N = 2 SQCD, including those with matter on external legs. Our results reveal chiral infrared-finite integrands closely related to those found using loop-level BCFW recursion. The integrands are valid in D <= 6 dimensions with external states in a four-dimensional subspace; the upper bound is dictated by our use of six-dimensional chiral N = (1, 0) SYM as a means of dimensionally regulating loop integrals.

Keywords
Duality in Gauge Field Theories, Scattering Amplitudes, Supersymmetric Gauge Theory
National Category
Subatomic Physics
Identifiers
urn:nbn:se:uu:diva-381768 (URN)10.1007/JHEP07(2019)120 (DOI)000476811300001 ()
Funder
Swedish Research Council, 621-2014-5722Knut and Alice Wallenberg Foundation, KAW 2013.0235EU, Horizon 2020, 746138
Available from: 2019-04-12 Created: 2019-04-12 Last updated: 2019-09-03Bibliographically approved
4. The Full-Color Two-Loop Four-Gluon Amplitude in N=2 Super-QCD
Open this publication in new window or tab >>The Full-Color Two-Loop Four-Gluon Amplitude in N=2 Super-QCD
Show others...
(English)Manuscript (preprint) (Other academic)
Abstract [en]

We present the fully integrated form of the two-loop four-gluon amplitude in N=2 supersymmetric quantum chromodynamics with gauge group SU(Nc) and with Nf massless supersymmetric quarks (hypermultiplets) in the fundamental representation. Our result maintains full dependence on Nc and Nf, and relies on the existence of a compact integrand representation that exhibits the duality between color and kinematics. Specializing to the N=2 superconformal theory, where Nf=2Nc , we obtain remarkably simple amplitudes that have an analytic structure close to that of N=4 super-Yang-Mills theory, except that now certain lower-weight terms appear. We comment on the corresponding results for other gauge groups.

National Category
Subatomic Physics
Identifiers
urn:nbn:se:uu:diva-381770 (URN)
Available from: 2019-04-12 Created: 2019-04-12 Last updated: 2019-04-16

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