3 definitions of BF theory on homology 3-spheres
Abstract 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 M $$ \mathcal{M} $$ of flat connections, weighted by the R...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-04-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP04(2023)146 |
| _version_ | 1827890587382054912 |
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| author | Matthias Blau Mbambu Kakona George Thompson |
| author_facet | Matthias Blau Mbambu Kakona George Thompson |
| author_sort | Matthias Blau |
| collection | DOAJ |
| description | Abstract 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 M $$ \mathcal{M} $$ 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 M $$ \mathcal{M} $$ 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 G ℂ 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. |
| first_indexed | 2024-03-12T21:12:49Z |
| format | Article |
| id | doaj.art-4d3c7c7151cc42a79bc579f6a1e0c8d7 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-12T21:12:49Z |
| publishDate | 2023-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-4d3c7c7151cc42a79bc579f6a1e0c8d72023-07-30T11:04:26ZengSpringerOpenJournal of High Energy Physics1029-84792023-04-012023414510.1007/JHEP04(2023)1463 definitions of BF theory on homology 3-spheresMatthias Blau0Mbambu Kakona1George Thompson2Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of BernEast African Institute for Fundamental Research (EAIFR), University of RwandaAbdus Salam International Centre for Theoretical PhysicsAbstract 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 M $$ \mathcal{M} $$ 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 M $$ \mathcal{M} $$ 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 G ℂ 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.https://doi.org/10.1007/JHEP04(2023)146Chern-Simons TheoriesTopological Field Theories |
| spellingShingle | Matthias Blau Mbambu Kakona George Thompson 3 definitions of BF theory on homology 3-spheres Journal of High Energy Physics Chern-Simons Theories Topological Field Theories |
| title | 3 definitions of BF theory on homology 3-spheres |
| title_full | 3 definitions of BF theory on homology 3-spheres |
| title_fullStr | 3 definitions of BF theory on homology 3-spheres |
| title_full_unstemmed | 3 definitions of BF theory on homology 3-spheres |
| title_short | 3 definitions of BF theory on homology 3-spheres |
| title_sort | 3 definitions of bf theory on homology 3 spheres |
| topic | Chern-Simons Theories Topological Field Theories |
| url | https://doi.org/10.1007/JHEP04(2023)146 |
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