Abstract
We use the variational principle approach to derive the large NN holographic dictionary for two-dimen-sional T\bar TTT‾-deformed CFTs, for both signs of the deformation parameter. The resulting dual gravitational theory has mixed boundary conditions for the non-dynamical graviton; the boundary conditions for matter fields are undeformed. When the matter fields are turned off and the deformation parameter is negative, the mixed boundary conditions for the metric at infinity can be reinterpreted on-shell as Dirichlet boundary conditions at finite bulk radius, in agreement with a previous proposal by McGough, Mezei and Verlinde. The holographic stress tensor of the deformed CFT is fixed by the variational principle, and in pure gravity it coincides with the Brown-York stress tensor on the radial bulk slice with a particular cosmological constant counterterm contribution. In presence of matter fields, the connection between the mixed boundary conditions and the radial ``bulk cutoff’’ is lost. Only the former correctly reproduce the energy of the bulk configuration, as expected from the fact that a universal formula for the deformed energy can only depend on the universal asymptotics of the bulk solution, rather than the details of its interior. The asymptotic symmetry group associated with the mixed boundary conditions consists of two commuting copies of a state-dependent Virasoro algebra, with the same central extension as in the original CFT.
Highlights
There has been plenty of recent interest in the T Tdeformation [1,2], a universal irrelevant deformation of two-dimensional QFTs
Even though the conformal symmetries of the original CFT are completely broken by the T Tdeformation, we interestingly find that the algebra of conserved charges in the deformed CFT still consists of two commuting copies of a Virasoro algebra, with the same central extension
We have provided a first-principles derivation of the holographic dictionary for T T-deformed CFTs at large N
Summary
There has been plenty of recent interest in the T Tdeformation [1,2], a universal irrelevant deformation of two-dimensional QFTs. We use the variational principle approach to show that at the level of classical gravity, the bulk dual to a T T-deformed holographic CFTs consists of the same gravitational theory as in the undeformed case, but with nonlinearly mixed boundary conditions for the boundary graviton, as expected from the fact that a double-trace deformation involving the stress tensor is turned on. These mixed boundary conditions, which are given explicitly in (2.28), hold for both signs of the deformation parameter and in presence of matter fields, provided only expectation values of the operators dual to them are turned on.
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