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Gluing Nekrasov partition functions
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.
2015 (English)In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 337, no 2, p. 785-816Article in journal (Refereed) Published
Abstract [en]

In this paper we summarise the localisation calculation of 5D superYang-Mills on simply connected toric Sasaki-Einstein (SE) manifolds. We showhow various aspects of the computation, including the equivariant index, theasymptotic behaviour and the factorisation property are governed by thecombinatorial data of the toric geometry. We prove that the full perturbativepartition function on a simply connected SE manifold corresponding to an n-gontoric diagram factorises to n copies of perturbative Nekrasov partitionfunction. This leads us to conjecture the full partition function as gluing ncopies of full Nekrasov partition function. This work is a generalisation ofsome earlier computation carried out on $Y^{p,q}$ manifolds, whose moment mapcone has a quadrangle and our result is valid for manifolds whose moment mapcones have pentagon base, hexagon base, etc. The algorithm we used for dealingwith general cones may also be of independent interest.

Place, publisher, year, edition, pages
2015. Vol. 337, no 2, p. 785-816
National Category
Subatomic Physics
Research subject
Theoretical Physics
Identifiers
URN: urn:nbn:se:uu:diva-252090DOI: 10.1007/s00220-015-2351-7ISI: 000353505300008OAI: oai:DiVA.org:uu-252090DiVA, id: diva2:808839
Note

Preprint number:  UUITP-02/14

Available from: 2015-04-29 Created: 2015-04-29 Last updated: 2018-04-02Bibliographically 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. p. 114
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
2. Topics in Five Dimensional Supersymmetry and Topological Quantum Field Theories
Open this publication in new window or tab >>Topics in Five Dimensional Supersymmetry and Topological Quantum Field Theories
2018 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

We explore five-dimensional supersymmetric quantum field theories and topological quantum field theories. In five dimensions, we describe a framework to consistently define a supersymmetric theory on a curved spacetime manifold. This is the starting point for the so called supersymmetric localization procedure which we exploit to compute the partition function on a large class of five-dimensional backgrounds. We discuss the geometric structure behind our result and analyze various extension of this program. Next, we present a seven-dimensional bulk topological field theory of abelian three-form potentials with a single derivative Chern-Simons-like action. We show how the edge modes can be understood from the perspective of a six-dimensional generalization of the fractional quantum Hall effect and compute an analog of the Laughlin wavefunction. We also explain why this has interesting implications for the study of six-dimensional superconformal field theories. Finally, we review a new approach to integrable lattice models in 1+1 dimensions based on a four-dimensional Chern-Simons-like theory and propose a strategy for its string theory embedding.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2018. p. 58
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1657
Keyword
Supersymmetric Quantum Field Theories, Topological Quantum Field Theories, String Theory.
National Category
Subatomic Physics
Identifiers
urn:nbn:se:uu:diva-347438 (URN)978-91-513-0301-7 (ISBN)
Public defence
2018-05-23, Häggsalen, Å10132, Campus Polacksbacken, Lägerhyddsv 1, Uppsala, 13:15 (English)
Opponent
Supervisors
Available from: 2018-05-03 Created: 2018-04-02 Last updated: 2018-05-03

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Publisher's full texthttp://arxiv.org/abs/1403.2945

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Tizzano, LuigiWinding, JacobZabzine, Maxim

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