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N=2 supersymmetric gauge theory on connected sums of S2xS2
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, 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.
2017 (English)In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, Vol. 03, 026Article in journal (Refereed) Published
Abstract [en]

We construct 4D N = 2 theories on an infinite family of 4D toric manifolds with the topology of connected sums of S-2 x S-2. These theories are constructed through the dimensional reduction along a non -trivial U(1) -fiber of 5D theories on toric Sasaki Einstein manifolds. We discuss the conditions under which such reductions can be carried out and give a partial classification result of the resulting 4D manifolds. We calculate the partition functions of these 4D theories and they involve both instanton and anti-instanton contributions, thus generalizing Pestun's famous result on S-4.

Place, publisher, year, edition, pages
2017. Vol. 03, 026
National Category
Subatomic Physics
Research subject
Theoretical Physics
Identifiers
URN: urn:nbn:se:uu:diva-318662DOI: 10.1007/JHEP03(2017)026ISI: 000397669900008OAI: oai:DiVA.org:uu-318662DiVA: diva2:1084901
Available from: 2017-03-27 Created: 2017-03-27 Last updated: 2017-04-19Bibliographically 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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