Blau, Matthias; Kakona, Mbambu; Thompson, George (2023). 3 definitions of BF theory on homology 3-spheres. Journal of High Energy Physics, 2023(4) Springer 10.1007/JHEP04(2023)146
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3-dimensional BF theory with gauge group G (= Chern-Simons theory with non-compact gauge group TG) is a deceptively simple yet subtle topological gauge theory. Formally, its partition function is a sum/integral over the moduli space of flat connections, weighted by the Ray-Singer torsion. In practice, however, this formal expression is almost invariably singular and ill-defined.
In order to improve upon this, we perform a direct evaluation of the path integral for certain classes of 3-manifolds (namely integral and rational Seifert homology spheres). By a suitable choice of gauge, we sidestep the issue of having to integrate over and reduce the partition function to a finite-dimensional Abelian matrix integral which, however, itself requires a definition. We offer 3 definitions of this integral, firstly via residues, and then via a large k limit of the corresponding G × G or Gℂ Chern-Simons matrix integrals (obtained previously). We then check and discuss to which extent the results capture the expected sum/integral over all flat connections.
Item Type: |
Journal Article (Original Article) |
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Division/Institute: |
08 Faculty of Science > Institute of Theoretical Physics 10 Strategic Research Centers > Albert Einstein Center for Fundamental Physics (AEC) |
UniBE Contributor: |
Blau, Matthias |
Subjects: |
500 Science > 530 Physics 500 Science |
ISSN: |
1029-8479 |
Publisher: |
Springer |
Language: |
English |
Submitter: |
Franziska Stämpfli |
Date Deposited: |
04 Dec 2023 10:23 |
Last Modified: |
04 Dec 2023 10:23 |
Publisher DOI: |
10.1007/JHEP04(2023)146 |
ArXiv ID: |
2211.10136 |
BORIS DOI: |
10.48350/189691 |
URI: |
https://boris.unibe.ch/id/eprint/189691 |
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