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Exact Results in Five-Dimensional Gauge Theories: On Supersymmetry, Localization and Matrix Models
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
2015 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Gauge theories are one of the corner stones of modern theoretical physics. They describe the nature of all fundamental interactions and have been applied in multiple branches of physics. The most challenging problem of gauge theories, which has not been solved yet, is their strong coupling dynamics. A class of gauge theories that admits simplifications allowing to deal with the strong coupling regime are supersymmetric ones. For example, recently proposed method of supersymmetric localization allows to reduce expectation values of supersymmetric observables, expressed through the path integral, to finite-dimensional matrix integral. The last one is usually easier to deal with compared to the original infinite-dimensional integral.

This thesis deals with the matrix models obtained from the localization of different 5D gauge theories. The focus of our study is N=1 super Yang-Mills theory with different matter content as well as N=1 Chern-Simons-Matter theory with adjoint hypermultiplets. Both theories are considered on the five-spheres. We make use of the saddle-point approximation of the matrix integrals, obtained from localization, to evaluate expectation values of different observables in these theories. This approximation corresponds to the large-N limit of the localized gauge theory.

We derive behavior for the free energy of 5D N=1* super Yang-Mills theory at strong coupling. This result is important in light of the relation between 5D theory and the world-volume theories of M5-branes, playing a significant role in string theory. We have also explored rich phase structure of 5D SU(N) N=1 super Yang-Mills theory coupled to massive matter in different representations of the gauge group. We have shown that in the case of the massive adjoint hypermultiplet theory undergoes infinite chain of the third order phase transitions while interpolating between weak and strong coupling in the decompactification limit.

Finally, we obtain several interesting results for 5D Chern-Simons theory, suggesting existence of the holographic duals to this theory. In particular, we derive  behavior of the free energy of this theory, which reproduces the behavior of the free energy for 5D theories with known  holographic duals.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2015. , 101 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1226
Keyword [en]
Supersymmetric localization, Matrix Models, Chern-Simons theory, Supersymmetric Field Theories, (2, 0) theories
National Category
Subatomic Physics
Research subject
Theoretical Physics
Identifiers
URN: urn:nbn:se:uu:diva-243320ISBN: 978-91-554-9164-2 (print)OAI: oai:DiVA.org:uu-243320DiVA: diva2:787023
Public defence
2015-03-27, Å80101, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, 13:15 (English)
Opponent
Supervisors
Available from: 2015-03-03 Created: 2015-02-08 Last updated: 2015-03-12Bibliographically approved
List of papers
1. N 3-behavior from 5D Yang-Mills theory
Open this publication in new window or tab >>N 3-behavior from 5D Yang-Mills theory
2012 (English)In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, Vol. 2012, no 10, 184- p.Article in journal (Refereed) Published
Abstract [en]

In this note we derive N 3-behavior at large 't Hooft coupling for the free energy of 5D maximally supersymmetric Yang-Mills theory on S 5. We also consider a Z κ quiver of this model, as well as a model with M hypermultiplets in the fundamental representation. We compare the results to the supergravity description and comment on their relation.

Keyword
1/N expansion, AdS-CFT correspondence, Matrix models, Strong coupling expansion
National Category
Natural Sciences
Identifiers
urn:nbn:se:uu:diva-184916 (URN)10.1007/JHEP10(2012)184 (DOI)000310851300015 ()
Available from: 2012-11-19 Created: 2012-11-15 Last updated: 2017-12-07Bibliographically approved
2. 5D super Yang-Mills theory and the correspondence to AdS(7)/CFT6
Open this publication in new window or tab >>5D super Yang-Mills theory and the correspondence to AdS(7)/CFT6
2013 (English)In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 46, no 35, 355401- p.Article in journal (Refereed) Published
Abstract [en]

We study the relation between 5D super Yang-Mills theory and the holographic description of 6D (2, 0) superconformal theory. We start by clarifying some issues related to the localization of N = 1 SYM with matter on S-5. We concentrate on the case of a single wadjoint hypermultiplet with a mass term and argue that the theory has a symmetry enlargement at mass M = 1/(2r), where r is the S-5 radius. However, in order to have a well-defined localization locus it is necessary to rotate M onto the imaginary axis, breaking the enlarged symmetry. Based on our prescription, the imaginary mass values are physical and we show how the localized path integral is consistent with earlier results for 5D SYM in flat space. We then compute the free energy and the expectation value for a circular Wilson loop in the large N limit. The Wilson loop calculation shows a mass dependent constant rescaling between weak and strong coupling. The Wilson loop continued back to to the enlarged symmetry point is consistent with a supergravity computation for an M2 brane using the standard identification of the compactification radius and the 5D coupling. If we continue back to the physical regime and use this value of the mass to determine the compactification radius, then we find agreement between the SYM free energy and the corresponding supergravity calculation. We also verify numerically some of our analytic approximations.

National Category
Natural Sciences
Identifiers
urn:nbn:se:uu:diva-207492 (URN)10.1088/1751-8113/46/35/355401 (DOI)000323201000012 ()
Available from: 2013-09-17 Created: 2013-09-16 Last updated: 2017-12-06Bibliographically approved
3. Phases of planar 5-dimensional supersymmetric Chern-Simons theory
Open this publication in new window or tab >>Phases of planar 5-dimensional supersymmetric Chern-Simons theory
2014 (English)In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, Vol. 12, 049- p.Article in journal (Refereed) Published
Abstract [en]

In this paper we investigate the large-N behavior of 5-dimensional N = 1 super Yang-Mills with a level k Chern-Simons term and an adjoint hypermultiplet. As in three-dimensional Chern-Simons theories, one must choose an integration contour to completely define the theory. Using localization, we reduce the path integral to a matrix model with a cubic action and compute its free energy in various scenarios. In the limit of infinite Yang-Mills coupling and for particular choices of the contours, we find that the free-energy scales as N-5/2 for U(N) gauge groups with large values of the Chern-Simons 't Hooft coupling, (lambda) over tilde = N/k. If we also set the hypermultiplet mass to zero, then this limit is a superconformal fixed point and the N-5/2 behavior parallels other fixed points which have known supergravity duals. We also demonstrate that SU(N) gauge groups cannot have this N-5/2 scaling for their free-energy. At finite Yang-Mills coupling we establish the existence of a third order phase transition where the theory crosses over from the Yang-Mills phase to the Chern-Simons phase. The phase transition exists for any value of (lambda) over tilde, although the details differ between small and large values of (lambda) over tilde. For pure Chern-Simons theories we present evidence for a chain of phase transitions as (lambda) over tilde is increased. We also find the expectation values for supersymmetric circular Wilson loops in these various scenarios and show that the Chern-Simons term leads to different physical properties for fundamental and anti-fundamentalWilson loops. Different choices of the integration contours also lead to different properties for the loops.

National Category
Subatomic Physics
Identifiers
urn:nbn:se:uu:diva-243312 (URN)10.1007/JHEP12(2014)049 (DOI)000348146400003 ()
Available from: 2015-02-08 Created: 2015-02-08 Last updated: 2017-12-04Bibliographically approved
4. Phase transitions in 5D super Yang-Mills theory
Open this publication in new window or tab >>Phase transitions in 5D super Yang-Mills theory
2015 (English)In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, Vol. 2015, no 7, 004Article in journal (Refereed) Published
Abstract [en]

In this paper we study a phase structure of 5D N=1 super Yang-Mills theory with massive matter multiplets and SU(N ) gauge group. In particular, we are interested in two cases: theory with N f massive hypermultiplets in the fundamental representation and theory with one adjoint massive hypermultiplet. If these theories are considered on S 5 their partition functions can be localized to matrix integrals, which can be approximated by their values at saddle points in the large-N limit. We solve saddle point equations corresponding to the decompactification limit of both theories. We find that in the case of the fundamental hypermultiplets theory experiences third-order phase transition when coupling is varied. We also show that in the case of one adjoint hypermultiplet theory experiences infinite chain of third-order phase transitions, while interpolating between weak and strong coupling regimes.

National Category
Subatomic Physics
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:uu:diva-243313 (URN)10.1007/JHEP07(2015)004 (DOI)000357329100002 ()
Available from: 2015-02-08 Created: 2015-02-08 Last updated: 2017-12-04Bibliographically approved

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