In this work we consider gravitational theory with certain mixed boundary conditions at infinity. Using the Chern-Simons formalism of gravity, we find that these mixed boundary conditions lead to nontrivial boundary terms, which, in turn, produce exactly the spectrum of the -deformed conformal field theories (CFTs). We then follow the procedure for constructing asymptotic boundary dynamics of to derive the constrained -deformed Wess-Zumino-Witten (WZW) model from Chern-Simons gravity. The resulting theory turns out to be the -deformed Alekseev-Shatashvili action after disentangling the constraints. Furthermore, by adding a gauge field associated to the current , we obtain one type of the -deformed WZW model, and show that its action can also be constructed from the gravity side. These results provide a check on the correspondence between the -deformed CFTs and the deformations of boundary conditions of , the latter of which may be regarded as coordinate transformations.
{ "_oai": { "updated": "2022-04-05T09:28:23Z", "id": "oai:repo.scoap3.org:62898", "sets": [ "PRD" ] }, "authors": [ { "raw_name": "Miao He", "affiliations": [ { "country": "China", "value": "School of Physical Sciences, University of Chinese Academy of Sciences, No.19A Yuquan Road, Beijing 100049, China" } ], "surname": "He", "given_names": "Miao", "full_name": "He, Miao" }, { "raw_name": "Yi-hong Gao", "affiliations": [ { "country": "China", "value": "CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China" } ], "surname": "Gao", "given_names": "Yi-hong", "full_name": "Gao, Yi-hong" } ], "titles": [ { "source": "APS", "title": "<math><mi>T</mi><mover><mi>T</mi><mo>\u00af</mo></mover><mo>/</mo><mi>J</mi><mover><mi>T</mi><mo>\u00af</mo></mover></math>-deformed WZW models from Chern-Simons <math><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></math> gravity with mixed boundary conditions" } ], "dois": [ { "value": "10.1103/PhysRevD.103.126019" } ], "publication_info": [ { "journal_volume": "103", "journal_title": "Physical Review D", "material": "article", "journal_issue": "12", "year": 2021 } ], "$schema": "http://repo.scoap3.org/schemas/hep.json", "acquisition_source": { "date": "2022-04-05T09:17:59.943839", "source": "APS", "method": "APS", "submission_number": "2cf5978cb4c111ec837fd6d834be26e1" }, "page_nr": [ 18 ], "license": [ { "url": "https://creativecommons.org/licenses/by/4.0/", "license": "CC-BY-4.0" } ], "copyright": [ { "statement": "Published by the American Physical Society", "year": "2021" } ], "control_number": "62898", "record_creation_date": "2021-06-17T20:30:03.495453", "_files": [ { "checksum": "md5:16e446d1bc410c7da911e6aa7860ad36", "filetype": "pdf", "bucket": "5b837c2a-ce04-4be5-825e-1ff6e33d90a1", "version_id": "d066aaf0-245c-4f0c-b6a5-caa7ca750349", "key": "10.1103/PhysRevD.103.126019.pdf", "size": 325697 }, { "checksum": "md5:f07c1978b4edfc44cec3d70e4a6929ab", "filetype": "xml", "bucket": "5b837c2a-ce04-4be5-825e-1ff6e33d90a1", "version_id": "cd42a937-9090-4edc-99cf-422d66625d6a", "key": "10.1103/PhysRevD.103.126019.xml", "size": 541455 } ], "collections": [ { "primary": "HEP" }, { "primary": "Citeable" }, { "primary": "Published" } ], "arxiv_eprints": [ { "categories": [ "hep-th", "gr-qc" ], "value": "2012.05726" } ], "abstracts": [ { "source": "APS", "value": "In this work we consider <math><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></math> gravitational theory with certain mixed boundary conditions at infinity. Using the Chern-Simons formalism of <math><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></math> gravity, we find that these mixed boundary conditions lead to nontrivial boundary terms, which, in turn, produce exactly the spectrum of the <math><mi>T</mi><mover><mi>T</mi><mo>\u00af</mo></mover><mo>/</mo><mi>J</mi><mover><mi>T</mi><mo>\u00af</mo></mover></math>-deformed conformal field theories (CFTs). We then follow the procedure for constructing asymptotic boundary dynamics of <math><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></math> to derive the constrained <math><mi>T</mi><mover><mi>T</mi><mo>\u00af</mo></mover></math>-deformed Wess-Zumino-Witten (WZW) model from Chern-Simons gravity. The resulting theory turns out to be the <math><mi>T</mi><mover><mi>T</mi><mo>\u00af</mo></mover></math>-deformed Alekseev-Shatashvili action after disentangling the constraints. Furthermore, by adding a <math><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></math> gauge field associated to the current <math><mi>J</mi></math>, we obtain one type of the <math><mi>J</mi><mover><mi>T</mi><mo>\u00af</mo></mover></math>-deformed WZW model, and show that its action can also be constructed from the gravity side. These results provide a check on the correspondence between the <math><mi>T</mi><mover><mi>T</mi><mo>\u00af</mo></mover><mo>/</mo><mi>J</mi><mover><mi>T</mi><mo>\u00af</mo></mover></math>-deformed CFTs and the deformations of boundary conditions of <math><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></math>, the latter of which may be regarded as coordinate transformations." } ], "imprints": [ { "date": "2021-06-17", "publisher": "APS" } ] }