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7D supersymmetric Yang-Mills on hypertoric 3-Sasakian manifolds
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
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.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.ORCID iD: 0000-0002-5845-2283
(English)Manuscript (preprint) (Other academic)
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:uu:diva-389898OAI: oai:DiVA.org:uu-389898DiVA, id: diva2:1339756
Available from: 2019-07-31 Created: 2019-07-31 Last updated: 2019-07-31
In thesis
1. 7D supersymmetric Yang-Mills theory on toric and hypertoric manifolds
Open this publication in new window or tab >>7D supersymmetric Yang-Mills theory on toric and hypertoric manifolds
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis consists of an introduction and three research papers in the general area of geometry and physics. In particular we study 7D supersymmetric Yang-Mills theory and related topics in toric and hypertoric geometry. Yang-Mills theory is used to describe particle interactions in physics but it also plays an important role in mathematics. For example, Yang-Mills theory can be used to formulate topological invariants in differential geometry. In Paper I we formulate 7D maximally supersymmetric Yang-Mills theory on curved manifolds that admit positive Killing spinors. For the case of Sasaki-Einstein manifolds we perform a localisation calculation and find the perturbative partition function of the theory. For toric Sasaki-Einstein manifolds we can write the answer in terms of a special function that count integer lattice points inside a cone determined by the toric action. In Papers II and III we consider 7D maximally supersymmetric Yang-Mills theory on hypertoric 3-Sasakian manifolds. We show that the perturbative partition function can again be formulated in terms of a special function counting integer lattice points in a cone, similar to the toric case. We also present a factorisation result for these functions.

Place, publisher, year, edition, pages
Uppsala: Department of Mathematics, 2019. p. 43
Series
Uppsala Dissertations in Mathematics, ISSN 1401-2049 ; 116
Keywords
Yang-Mills theory, supersymmetry, toric geometry, hypertoric geometry, Sasaki-Einstein, 3-Sasaki, localisation, special functions
National Category
Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:uu:diva-389899 (URN)978-91-506-2780-0 (ISBN)
Public defence
2019-09-20, Å4001, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, 10:00 (English)
Opponent
Supervisors
Available from: 2019-08-28 Created: 2019-07-31 Last updated: 2019-08-28

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Qiu, JianRocén, AndreasZabzine, Maxim

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