TT¯/JT¯-deformed WZW models from Chern-Simons AdS3 gravity with mixed boundary conditions

Miao He (School of Physical Sciences, University of Chinese Academy of Sciences, No.19A Yuquan Road, Beijing 100049, China) ; Yi-hong Gao (CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China)

In this work we consider AdS3 gravitational theory with certain mixed boundary conditions at infinity. Using the Chern-Simons formalism of AdS3 gravity, we find that these mixed boundary conditions lead to nontrivial boundary terms, which, in turn, produce exactly the spectrum of the TT¯/JT¯-deformed conformal field theories (CFTs). We then follow the procedure for constructing asymptotic boundary dynamics of AdS3 to derive the constrained TT¯-deformed Wess-Zumino-Witten (WZW) model from Chern-Simons gravity. The resulting theory turns out to be the TT¯-deformed Alekseev-Shatashvili action after disentangling the constraints. Furthermore, by adding a U(1) gauge field associated to the current J, we obtain one type of the JT¯-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 TT¯/JT¯-deformed CFTs and the deformations of boundary conditions of AdS3, the latter of which may be regarded as coordinate transformations.

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      "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."
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Published on:
17 June 2021
Publisher:
APS
Published in:
Physical Review D , Volume 103 (2021)
Issue 12
DOI:
https://doi.org/10.1103/PhysRevD.103.126019
arXiv:
2012.05726
Copyrights:
Published by the American Physical Society
Licence:
CC-BY-4.0

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