TT deformations in general dimensions

By Marika Taylor. 2018

184 citations recorded by the source corpus.

It has recently been proposed that Zamoldchikov's $T \bar{T}$ deformation of two-dimensional CFTs describes the holographic theory dual to AdS$_3$ at finite radius. In this note we use the Gauss-Codazzi form of 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 $T \bar{T}$ 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 $T \bar{T}$. 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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8ee7b8719d330f76f6e47e5164baeb4a4a10b699

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Citations in the corpus

Holography at finite cutoff with a T2 deformation (2018, background): “ve deﬁnition for the theory on Minkowski spacetime is provided by the 4 S-matrix [12], or at c = 24 with certain sign of the coupling by critical string theory [38]. As this work was being completed, [36] appeared, which also derives the source-free versions of equation (1.1) and the corresponding e”