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7D supersymmetric Yang-Mills theory on toric and hypertoric manifoldsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2019 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Description

##### Abstract [en]

##### 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

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##### Supervisors

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt507",{id:"formSmash:j_idt507",widgetVar:"widget_formSmash_j_idt507",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt513",{id:"formSmash:j_idt513",widgetVar:"widget_formSmash_j_idt513",multiple:true}); Available from: 2019-08-28 Created: 2019-07-31 Last updated: 2019-08-28
##### List of papers

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.

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isbn
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