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Phase transitions in 5D super Yang-Mills theory
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
2015 (English)In: Journal of High Energy Physics (JHEP), ISSN 1029-8479, E-ISSN 1126-6708, 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.

##### Place, publisher, year, edition, pages
2015. Vol. 2015, no 7, 004
##### National Category
Subatomic Physics
##### Research subject
Theoretical Physics
##### Identifiers
ISI: 000357329100002OAI: oai:DiVA.org:uu-243313DiVA: diva2:786996
Available from: 2015-02-08 Created: 2015-02-08 Last updated: 2015-08-11Bibliographically 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 $N^{3}$ 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 $N^{5/2}$ 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)
##### Supervisors
Available from: 2015-03-03 Created: 2015-02-08 Last updated: 2015-03-12Bibliographically approved

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