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7D supersymmetric Yang-Mills theory on toric and hypertoric manifolds
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Description
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 [en]
Yang-Mills theory, supersymmetry, toric geometry, hypertoric geometry, Sasaki-Einstein, 3-Sasaki, localisation, special functions
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-389899ISBN: 978-91-506-2780-0 (print)OAI: oai:DiVA.org:uu-389899DiVA, id: diva2:1339768
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
List of papers
1. 7D supersymmetric Yang-Mills on curved manifolds
Open this publication in new window or tab >>7D supersymmetric Yang-Mills on curved manifolds
2017 (English)In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, no 12, article id 152Article in journal (Refereed) Published
Abstract [en]

We study 7D maximally supersymmetric Yang-Mills theory on curved manifolds that admit Killing spinors. If the manifold admits at least two Killing spinors (Sasaki-Einstein manifolds) we are able to rewrite the supersymmetric theory in terms of a cohomological complex. In principle this cohomological complex makes sense for any K-contact manifold. For the case of toric Sasaki-Einstein manifolds we derive explicitly the perturbative part of the partition function and speculate about the non-perturbative part. We also briefly discuss the case of 3-Sasaki manifolds and suggest a plausible form for the full non-perturbative answer.

Place, publisher, year, edition, pages
Springer, 2017
Keywords
Differential and Algebraic Geometry, Supersymmetric Gauge Theory
National Category
Physical Sciences
Identifiers
urn:nbn:se:uu:diva-340461 (URN)10.1007/JHEP12(2017)152 (DOI)000419111400010 ()
Available from: 2018-02-15 Created: 2018-02-15 Last updated: 2019-07-31Bibliographically approved
2. 7D supersymmetric Yang-Mills on a 3-Sasakian manifold
Open this publication in new window or tab >>7D supersymmetric Yang-Mills on a 3-Sasakian manifold
2018 (English)In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, no 11, article id 024Article in journal (Refereed) Published
Abstract [en]

In this paper we study 7D maximally supersymmetric Yang-Mills on a specific 3-Sasakian manifold that is the total space of an SO(3)-bundle over CP2. The novelty of this example is that the manifold is not a toric Sasaki-Einstein manifold. The hyperkahler cone of this manifold is a Swann bundle with hypertoric symmetry and this allows us to calculate the perturbative part of the partition function of the theory. The result is also verified by an index calculation. We also discuss a factorisation of this result and compare it with analogous results for S-7.

Place, publisher, year, edition, pages
SPRINGER, 2018
Keywords
Differential and Algebraic Geometry, Field Theories in Higher Dimensions, Supersymmetric Gauge Theory
National Category
Mathematics
Identifiers
urn:nbn:se:uu:diva-369394 (URN)10.1007/JHEP11(2018)024 (DOI)000449411400001 ()
Funder
Knut and Alice Wallenberg Foundation
Available from: 2019-01-14 Created: 2019-01-14 Last updated: 2019-07-31Bibliographically approved
3. 7D supersymmetric Yang-Mills on hypertoric 3-Sasakian manifolds
Open this publication in new window or tab >>7D supersymmetric Yang-Mills on hypertoric 3-Sasakian manifolds
(English)Manuscript (preprint) (Other academic)
National Category
Physical Sciences
Identifiers
urn:nbn:se:uu:diva-389898 (URN)
Available from: 2019-07-31 Created: 2019-07-31 Last updated: 2019-07-31

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