2D gravitational Mabuchi action on Riemann surfaces with boundaries
Abstract We study the gravitational action induced by coupling two-dimensional non-conformal, massive matter to gravity on a Riemann surface with boundaries. A small-mass expansion gives back the Liouville action in the massless limit, while the first-order mass correction allows us to identify what...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-11-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP11(2017)154 |
| _version_ | 1828476294229131264 |
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| author | Adel Bilal Corinne de Lacroix |
| author_facet | Adel Bilal Corinne de Lacroix |
| author_sort | Adel Bilal |
| collection | DOAJ |
| description | Abstract We study the gravitational action induced by coupling two-dimensional non-conformal, massive matter to gravity on a Riemann surface with boundaries. A small-mass expansion gives back the Liouville action in the massless limit, while the first-order mass correction allows us to identify what should be the appropriate generalization of the Mabuchi action on a Riemann surface with boundaries. We provide a detailed study for the example of the cylinder. Contrary to the case of manifolds without boundary, we find that the gravitational Lagrangian explicitly depends on the space-point, via the geodesic distances to the boundaries, as well as on the modular parameter of the cylinder, through an elliptic θ-function. |
| first_indexed | 2024-12-11T06:26:41Z |
| format | Article |
| id | doaj.art-4ae807a88f464345992b64b7bb3d9b4c |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-11T06:26:41Z |
| publishDate | 2017-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-4ae807a88f464345992b64b7bb3d9b4c2022-12-22T01:17:38ZengSpringerOpenJournal of High Energy Physics1029-84792017-11-0120171113510.1007/JHEP11(2017)1542D gravitational Mabuchi action on Riemann surfaces with boundariesAdel Bilal0Corinne de Lacroix1Laboratoire de Physique Théorique de l’ École Normale Supérieure, PSL Research University, CNRS, Sorbonne Universités, UPMC Paris 6Laboratoire de Physique Théorique de l’ École Normale Supérieure, PSL Research University, CNRS, Sorbonne Universités, UPMC Paris 6Abstract We study the gravitational action induced by coupling two-dimensional non-conformal, massive matter to gravity on a Riemann surface with boundaries. A small-mass expansion gives back the Liouville action in the massless limit, while the first-order mass correction allows us to identify what should be the appropriate generalization of the Mabuchi action on a Riemann surface with boundaries. We provide a detailed study for the example of the cylinder. Contrary to the case of manifolds without boundary, we find that the gravitational Lagrangian explicitly depends on the space-point, via the geodesic distances to the boundaries, as well as on the modular parameter of the cylinder, through an elliptic θ-function.http://link.springer.com/article/10.1007/JHEP11(2017)1542D GravityModels of Quantum Gravity |
| spellingShingle | Adel Bilal Corinne de Lacroix 2D gravitational Mabuchi action on Riemann surfaces with boundaries Journal of High Energy Physics 2D Gravity Models of Quantum Gravity |
| title | 2D gravitational Mabuchi action on Riemann surfaces with boundaries |
| title_full | 2D gravitational Mabuchi action on Riemann surfaces with boundaries |
| title_fullStr | 2D gravitational Mabuchi action on Riemann surfaces with boundaries |
| title_full_unstemmed | 2D gravitational Mabuchi action on Riemann surfaces with boundaries |
| title_short | 2D gravitational Mabuchi action on Riemann surfaces with boundaries |
| title_sort | 2d gravitational mabuchi action on riemann surfaces with boundaries |
| topic | 2D Gravity Models of Quantum Gravity |
| url | http://link.springer.com/article/10.1007/JHEP11(2017)154 |
| work_keys_str_mv | AT adelbilal 2dgravitationalmabuchiactiononriemannsurfaceswithboundaries AT corinnedelacroix 2dgravitationalmabuchiactiononriemannsurfaceswithboundaries |