Kac-Moody and Virasoro characters from the perturbative Chern-Simons path integral
Abstract We evaluate to one loop the functional integral that computes the partition functions of Chern-Simons theories based on compact groups, using the background field method and a covariant gauge fixing. We compare our computation with the results of other, less direct methods. We find that our...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-05-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP05(2019)083 |
| _version_ | 1818307978129833984 |
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| author | Massimo Porrati Cedric Yu |
| author_facet | Massimo Porrati Cedric Yu |
| author_sort | Massimo Porrati |
| collection | DOAJ |
| description | Abstract We evaluate to one loop the functional integral that computes the partition functions of Chern-Simons theories based on compact groups, using the background field method and a covariant gauge fixing. We compare our computation with the results of other, less direct methods. We find that our method correctly computes the characters of irreducible representations of Kac-Moody algebras. To extend the computation to non-compact groups we need to perform an appropriate analytic continuation of the partition function of the compact group. Non-vacuum characters are found by inserting a Wilson loop in the functional integral. We then extend our method to Euclidean Anti-de Sitter pure gravity in three dimensions. The explicit computation unveils several interesting features and lessons. The most important among them is that the very definition of gravity in the first-order Chern-Simons formalism requires non-trivial analytic continuations of the gauge fields outside their original domains of definition. |
| first_indexed | 2024-12-13T07:06:58Z |
| format | Article |
| id | doaj.art-8593f17855e24278939f5312369cf62c |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-13T07:06:58Z |
| publishDate | 2019-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-8593f17855e24278939f5312369cf62c2022-12-21T23:55:47ZengSpringerOpenJournal of High Energy Physics1029-84792019-05-012019517110.1007/JHEP05(2019)083Kac-Moody and Virasoro characters from the perturbative Chern-Simons path integralMassimo Porrati0Cedric Yu1Center for Cosmology and Particle Physics, Department of Physics, New York UniversityCenter for Cosmology and Particle Physics, Department of Physics, New York UniversityAbstract We evaluate to one loop the functional integral that computes the partition functions of Chern-Simons theories based on compact groups, using the background field method and a covariant gauge fixing. We compare our computation with the results of other, less direct methods. We find that our method correctly computes the characters of irreducible representations of Kac-Moody algebras. To extend the computation to non-compact groups we need to perform an appropriate analytic continuation of the partition function of the compact group. Non-vacuum characters are found by inserting a Wilson loop in the functional integral. We then extend our method to Euclidean Anti-de Sitter pure gravity in three dimensions. The explicit computation unveils several interesting features and lessons. The most important among them is that the very definition of gravity in the first-order Chern-Simons formalism requires non-trivial analytic continuations of the gauge fields outside their original domains of definition.http://link.springer.com/article/10.1007/JHEP05(2019)083Chern-Simons TheoriesConformal and W SymmetryWilson, ’t Hooft and Polyakov loopsAdS-CFT Correspondence |
| spellingShingle | Massimo Porrati Cedric Yu Kac-Moody and Virasoro characters from the perturbative Chern-Simons path integral Journal of High Energy Physics Chern-Simons Theories Conformal and W Symmetry Wilson, ’t Hooft and Polyakov loops AdS-CFT Correspondence |
| title | Kac-Moody and Virasoro characters from the perturbative Chern-Simons path integral |
| title_full | Kac-Moody and Virasoro characters from the perturbative Chern-Simons path integral |
| title_fullStr | Kac-Moody and Virasoro characters from the perturbative Chern-Simons path integral |
| title_full_unstemmed | Kac-Moody and Virasoro characters from the perturbative Chern-Simons path integral |
| title_short | Kac-Moody and Virasoro characters from the perturbative Chern-Simons path integral |
| title_sort | kac moody and virasoro characters from the perturbative chern simons path integral |
| topic | Chern-Simons Theories Conformal and W Symmetry Wilson, ’t Hooft and Polyakov loops AdS-CFT Correspondence |
| url | http://link.springer.com/article/10.1007/JHEP05(2019)083 |
| work_keys_str_mv | AT massimoporrati kacmoodyandvirasorocharactersfromtheperturbativechernsimonspathintegral AT cedricyu kacmoodyandvirasorocharactersfromtheperturbativechernsimonspathintegral |