Gravitational path integral from the T 2 deformation
Abstract We study a T 2 deformation of large N conformal field theories, a higher dimensional generalization of the T T ¯ $$ T\overline{T} $$ deformation. The deformed partition function satisfies a flow equation of the diffusion type. We solve this equation by finding its diffusion kernel, which is...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-09-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP09(2020)156 |
| _version_ | 1819011104568770560 |
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| author | Alexandre Belin Aitor Lewkowycz Gábor Sárosi |
| author_facet | Alexandre Belin Aitor Lewkowycz Gábor Sárosi |
| author_sort | Alexandre Belin |
| collection | DOAJ |
| description | Abstract We study a T 2 deformation of large N conformal field theories, a higher dimensional generalization of the T T ¯ $$ T\overline{T} $$ deformation. The deformed partition function satisfies a flow equation of the diffusion type. We solve this equation by finding its diffusion kernel, which is given by the Euclidean gravitational path integral in d + 1 dimensions between two boundaries with Dirichlet boundary conditions for the metric. This is natural given the connection between the flow equation and the Wheeler-DeWitt equation, on which we offer a new perspective by giving a gauge-invariant relation between the deformed partition function and the radial WDW wave function. An interesting output of the flow equation is the gravitational path integral measure which is consistent with a constrained phase space quantization. Finally, we comment on the relation between the radial wave function and the Hartle-Hawking wave functions dual to states in the CFT, and propose a way of obtaining the volume of the maximal slice from the T 2 deformation. |
| first_indexed | 2024-12-21T01:22:51Z |
| format | Article |
| id | doaj.art-4b561c68c6d84daa9df99b5507cc8bb9 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-21T01:22:51Z |
| publishDate | 2020-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-4b561c68c6d84daa9df99b5507cc8bb92022-12-21T19:20:35ZengSpringerOpenJournal of High Energy Physics1029-84792020-09-012020913210.1007/JHEP09(2020)156Gravitational path integral from the T 2 deformationAlexandre Belin0Aitor Lewkowycz1Gábor Sárosi2CERN, Theory DivisionStanford Institute for Theoretical Physics, Department of Physics, Stanford UniversityCERN, Theory DivisionAbstract We study a T 2 deformation of large N conformal field theories, a higher dimensional generalization of the T T ¯ $$ T\overline{T} $$ deformation. The deformed partition function satisfies a flow equation of the diffusion type. We solve this equation by finding its diffusion kernel, which is given by the Euclidean gravitational path integral in d + 1 dimensions between two boundaries with Dirichlet boundary conditions for the metric. This is natural given the connection between the flow equation and the Wheeler-DeWitt equation, on which we offer a new perspective by giving a gauge-invariant relation between the deformed partition function and the radial WDW wave function. An interesting output of the flow equation is the gravitational path integral measure which is consistent with a constrained phase space quantization. Finally, we comment on the relation between the radial wave function and the Hartle-Hawking wave functions dual to states in the CFT, and propose a way of obtaining the volume of the maximal slice from the T 2 deformation.http://link.springer.com/article/10.1007/JHEP09(2020)156AdS-CFT CorrespondenceGauge-gravity correspondence |
| spellingShingle | Alexandre Belin Aitor Lewkowycz Gábor Sárosi Gravitational path integral from the T 2 deformation Journal of High Energy Physics AdS-CFT Correspondence Gauge-gravity correspondence |
| title | Gravitational path integral from the T 2 deformation |
| title_full | Gravitational path integral from the T 2 deformation |
| title_fullStr | Gravitational path integral from the T 2 deformation |
| title_full_unstemmed | Gravitational path integral from the T 2 deformation |
| title_short | Gravitational path integral from the T 2 deformation |
| title_sort | gravitational path integral from the t 2 deformation |
| topic | AdS-CFT Correspondence Gauge-gravity correspondence |
| url | http://link.springer.com/article/10.1007/JHEP09(2020)156 |
| work_keys_str_mv | AT alexandrebelin gravitationalpathintegralfromthet2deformation AT aitorlewkowycz gravitationalpathintegralfromthet2deformation AT gaborsarosi gravitationalpathintegralfromthet2deformation |