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5D super Yang-Mills theory and the correspondence to AdS(7)/CFT6
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
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.

Place, publisher, year, edition, pages
2013. Vol. 46, no 35, 355401- p.
National Category
Natural Sciences
Identifiers
URN: urn:nbn:se:uu:diva-207492DOI: 10.1088/1751-8113/46/35/355401ISI: 000323201000012OAI: oai:DiVA.org:uu-207492DiVA: diva2:648932
Available from: 2013-09-17 Created: 2013-09-16 Last updated: 2017-12-06Bibliographically approved
In thesis
1. Exact Results in Five-Dimensional Gauge Theories: On Supersymmetry, Localization and Matrix Models
Open this publication in new window or tab >>Exact Results in Five-Dimensional Gauge Theories: On Supersymmetry, Localization and Matrix Models
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
Supersymmetric localization, Matrix Models, Chern-Simons theory, Supersymmetric Field Theories, (2, 0) theories
National Category
Subatomic Physics
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:uu:diva-243320 (URN)978-91-554-9164-2 (ISBN)
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

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Minahan, Joseph A.Nedelin, AntonZabzine, Maxim

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