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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, 785-816 p.Article 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, 785-816 p.
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: diva2:808839
Note

Preprint number:  UUITP-02/14

Available from: 2015-04-29 Created: 2015-04-29 Last updated: 2017-12-04Bibliographically 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 texthttp://arxiv.org/abs/1403.2945

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Tizzano, LuigiWinding, JacobZabzine, Maxim

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