Digitala Vetenskapliga Arkivet

Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Topics in Cohomological Field Theory: Let's Twist Again!
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
2025 (English)Doctoral thesis, comprehensive summary (Other academic)
Description
Abstract [en]

This thesis explores different aspects of cohomologically twisted supersymmetric field theories. Compared to their untwisted cousins, these theories are characterised by the existence of a BRST-like fermionic symmetry, and observables are considered elements in its cohomology. The partition and correlation functions of such theories can be computed exactly by applying supersymmetric localisation. Employing this formalism, in the first part we compute the partition function of 4d N=2 pure gauge theory on a large class of manifolds with non-trivial two-cycles, accounting for flux contributions. The main idea is to obtain this theory from the 5d N=1 pure gauge theory as a limit of finite quotients along a free circle. We repeat this analysis, mutatis mutandis, for a case where the circle action is only locally free, starting from a resolved branched five-sphere. The result suggests a close relation with a corresponding theory on weighted projective space. In the second part, we study an equivariant deformation of the B model on the sphere. As a main feature, this model allows for new, position-dependent observables that have no counterpart in the standard B model. Two such observables—position-dependent superpotentials and complex structure deformations—are studied in detail.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2025. , p. 100
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 2526
Keywords [en]
Supersymmetry, Localisation, Cohomological Field Theory
National Category
Physical Sciences
Research subject
Theoretical Physics
Identifiers
URN: urn:nbn:se:uu:diva-553153ISBN: 978-91-513-2454-8 (print)OAI: oai:DiVA.org:uu-553153DiVA, id: diva2:1948428
Public defence
2025-05-26, room 101121, Ångströmlaboratoriet, Regementsvägen 10, Uppsala, 13:15 (English)
Opponent
Supervisors
Available from: 2025-04-29 Created: 2025-03-29 Last updated: 2025-04-29
List of papers
1. From 5d flat connections to 4d fluxes (the art of slicing the cone)
Open this publication in new window or tab >>From 5d flat connections to 4d fluxes (the art of slicing the cone)
2023 (English)In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, Vol. 2023, no 10, article id 155Article in journal (Refereed) Published
National Category
Physical Sciences
Identifiers
urn:nbn:se:uu:diva-553140 (URN)10.1007/jhep10(2023)155 (DOI)
Available from: 2025-03-24 Created: 2025-03-24 Last updated: 2025-03-29
2. Super Yang-Mills on branched covers and weighted projective spaces
Open this publication in new window or tab >>Super Yang-Mills on branched covers and weighted projective spaces
2024 (English)In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, no 8, article id 106Article in journal (Refereed) Published
Abstract [en]

In this work we conjecture the Coulomb branch partition function, including flux and instanton contributions, for the N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N} $$\end{document} = 2 vector multiplet on weighted projective space CPN2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\mathbbm{CP}}_N<^>2 $$\end{document} for equivariant Donaldson-Witten and "Pestun-like" theories. More precisely, we claim that this partition function agrees with the one computed on a certain branched cover of CP2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\mathbbm{CP}}<^>2 $$\end{document} upon matching conical deficit angles with corresponding branch indices. Our conjecture is substantiated by checking that similar partition functions on spindles agree with their equivalent on certain branched covers of CP1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\mathbbm{CP}}<^>1 $$\end{document}. We compute the one-loop determinant on the branched cover of CP2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\mathbbm{CP}}<^>2 $$\end{document} for all flux sectors via dimensional reduction from the N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N} $$\end{document} = 1 vector multiplet on a branched five-sphere along a free S1-action. This work paves the way for obtaining partition functions on more generic symplectic toric orbifolds.

Place, publisher, year, edition, pages
Springer, 2024
Keywords
Nonperturbative Effects, Supersymmetric Gauge Theory, Extended Supersymmetry
National Category
Subatomic Physics
Identifiers
urn:nbn:se:uu:diva-537759 (URN)10.1007/JHEP08(2024)106 (DOI)001291605900002 ()
Available from: 2024-09-17 Created: 2024-09-17 Last updated: 2025-04-08Bibliographically approved
3. The Equivariant B model
Open this publication in new window or tab >>The Equivariant B model
(English)Manuscript (preprint) (Other academic)
National Category
Physical Sciences
Identifiers
urn:nbn:se:uu:diva-553142 (URN)
Available from: 2025-03-24 Created: 2025-03-24 Last updated: 2025-03-29

Open Access in DiVA

UUThesis_R-Mauch-2025(758 kB)49 downloads
File information
File name FULLTEXT01.pdfFile size 758 kBChecksum SHA-512
7bdf56f2b97a3b265a51be7e47f9d835e9efcd181a50db0e7330bcda33d5c62044f03abc1fd709b358bbd4b70c1fd0b1db27ca4871077e670c1b98df17712c1a
Type fulltextMimetype application/pdf

Search in DiVA

By author/editor
Mauch, Roman
By organisation
Theoretical Physics
Physical Sciences

Search outside of DiVA

GoogleGoogle Scholar
Total: 49 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

isbn
urn-nbn

Altmetric score

isbn
urn-nbn
Total: 404 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf