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Modular properties of full 5D SYM partition function
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
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.
2016 (English)In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, Vol. 16, no 03, 193Article in journal (Refereed) Published
Abstract [en]

We study properties of the full partition function for the U(1) 5D N=2∗ gauge theory with adjoint hypermultiplet of mass M. This theory is ultimately related to abelian 6D (2,0) theory. We construct the full non-perturbative partition function on toric Sasaki-Einstein manifolds by gluing flat copies of the Nekrasov partition function and we express the full partition function in terms of the generalized double elliptic gamma function GC2 associated with a certain moment map cone C. The answer exhibits a curious SL(4,ℤ) modular property. Finally, we propose a set of rules to construct the partition function that resembles the calculation of 5D supersymmetric partition function with the insertion of defects of various co-dimensions.

Place, publisher, year, edition, pages
2016. Vol. 16, no 03, 193
National Category
Subatomic Physics
Research subject
Theoretical Physics
Identifiers
URN: urn:nbn:se:uu:diva-287828DOI: 10.1007/JHEP03(2016)193ISI: 000373391900002OAI: oai:DiVA.org:uu-287828DiVA: diva2:923519
Funder
Swedish Research Council, 2014-5517The Swedish Foundation for International Cooperation in Research and Higher Education (STINT)Knut and Alice Wallenberg Foundation
Available from: 2016-04-26 Created: 2016-04-26 Last updated: 2017-04-03Bibliographically approved
In thesis
1. Localization, supersymmetric gauge theories and toric geometry
Open this publication in new window or tab >>Localization, supersymmetric gauge theories and toric geometry
2017 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Gauge theories is one of the most pervasive and important subject of modern theoretical physics, and there are still many things about them we do not understand. In particular dealing with strongly coupled theories where normal perturbative techniques do not apply is a fundamental open problem. In this thesis, we study a particular class of toy-models that have supersymmetry, which makes them much easier to deal with. We employ the mathematical technique of localization, which for supersymmetric theories lets us evaluate certain path integrals exactly and for any value of the coupling. This is used to study the 5d N=1 theories placed on toric Sasaki-Einstein manifolds and compute their partition functions, finding that they factorize into a product of contributions from each closed Reeb orbit of the manifold. This computation leads us to define two new hierarchies of special functions associated to these manifolds, and we study their properties. Finally, we use the 5d N=1 theories to construct new 4d N=2 theories on a large class of curved backgrounds. These theories have some interesting features, such as supporting both instantons and anti-instantons, and having a position-dependent complexified coupling constant.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2017. 114 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1500
Keyword
Supersymmetry, gauge theory, localization, toric geometry
National Category
Subatomic Physics
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:uu:diva-318668 (URN)978-91-554-9882-5 (ISBN)
Public defence
2017-05-26, Häggsalen, Ångströmslaboratoriet, Lägerhyddsvägen 1, Uppsala, 10:00 (English)
Opponent
Supervisors
Available from: 2017-05-02 Created: 2017-04-03 Last updated: 2017-05-05

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Publisher's full textarXiv:1511.06304 [hep-th]

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