TT deformations in general dimensions
TT deformations in general dimensions
It has recently been proposed that Zamoldchikov’s TT deformationof two-dimensional CFTs describes the holographic theory dual toAdS3 at finite radius. In this note we use the Gauss-Codazzi formof the Einstein equations to derive a relationship in general dimensions between the trace of the quasi-local stress tensor and a specific quadratic combination of this stress tensor, on constant radius slices of AdS. We use this relation to propose a generalization of Zamoldchikov’s TT deformation to conformal field theories in general dimensions. This operator is quadratic in the stress tensor and retains many but not all of the features of TT. To describe gravity with gauge or scalar fields, the deforming operator needs to be modified to include appropriate terms involving the corresponding R currents and scalar operators and we can again use the Gauss-Codazzi form of the Einstein equations to deduce the forms of the deforming operators. We conclude by discussing the relation of the quadratic stress tensor deformation to the stress energy tensor trace constraint in holographic theories dual to vacuum Einstein gravity.
37-63
Taylor, Marika
5515acab-1bed-4607-855a-9e04252aec22
Taylor, Marika
5515acab-1bed-4607-855a-9e04252aec22
Taylor, Marika
(2023)
TT deformations in general dimensions.
Advances in Theoretical and Mathematical Physics, 27 (1), .
(doi:10.4310/ATMP.2023.v27.n1.a2).
Abstract
It has recently been proposed that Zamoldchikov’s TT deformationof two-dimensional CFTs describes the holographic theory dual toAdS3 at finite radius. In this note we use the Gauss-Codazzi formof the Einstein equations to derive a relationship in general dimensions between the trace of the quasi-local stress tensor and a specific quadratic combination of this stress tensor, on constant radius slices of AdS. We use this relation to propose a generalization of Zamoldchikov’s TT deformation to conformal field theories in general dimensions. This operator is quadratic in the stress tensor and retains many but not all of the features of TT. To describe gravity with gauge or scalar fields, the deforming operator needs to be modified to include appropriate terms involving the corresponding R currents and scalar operators and we can again use the Gauss-Codazzi form of the Einstein equations to deduce the forms of the deforming operators. We conclude by discussing the relation of the quadratic stress tensor deformation to the stress energy tensor trace constraint in holographic theories dual to vacuum Einstein gravity.
Text
2-Taylor
- Accepted Manuscript
More information
Accepted/In Press date: 6 June 2023
e-pub ahead of print date: 13 July 2023
Additional Information:
Funding Information:
This work is funded by the STFC grant ST/P000711/1. This project has received funding and support from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 690575. MMT would like to thank the Kavli Institute for the Physics and Mathematics of the Universe and the Banff International Research Station for hospitality during the completion of this work.
Identifiers
Local EPrints ID: 481067
URI: http://eprints.soton.ac.uk/id/eprint/481067
ISSN: 1095-0761
PURE UUID: 8f79c8b8-5417-4911-b2c5-5f479c5e2f9f
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Date deposited: 15 Aug 2023 16:44
Last modified: 06 Jun 2024 01:50
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