Asymptotic Symmetries in the TsT/$T\bar{T}$ Correspondence

Abstract

Starting from holography for IIB string theory on AdS${}_3\times \mathcal{N}$ with NS-NS flux, the TsT/$T\bar{T}$ correspondence is a conjecture that a TsT transformation on the string theory side is holographically dual to the single-trace version of the $T\bar{T}$ deformation on the field theory side. More precisely, the long string sector of string theory on the TsT-transformed background corresponds to the symmetric product theory whose seed theory is the $T\bar{T}$-deformed CFT${}_2$. In this paper, we study the asymptotic symmetry of the string theory in the bulk. We find a state-dependent, non-local field redefinition under which the worldsheet equations of motion, stress tensor, as well as the symplectic form of string theory after the TsT transformation are mapped to those before the TsT transformation. The asymptotic symmetry in the auxiliary AdS basis is generated by two commuting Virasoro generators, while in the TsT transformed basis is non-linear and non-local. Our result from string theory analysis is compatible with that of the $T\bar{T}$ deformed CFT${}_2$.

32 pages; added clarifications, matches published version

References in corpus (17)

• On space of integrable quantum field theories
• $T\bar{T}$-deformed 2D Quantum Field Theories
• Solving the Simplest Theory of Quantum Gravity
• A Solvable Irrelevant Deformation of $Ad{S}_3/CF{T}_2$
• A perturbative CFT dual for pure NS-NS AdS${}_3$ strings
• Expectation value of composite field $T\bar{T}$ in two-dimensional quantum field theory
• Lectures on Celestial Holography
• Correlation Functions in $\text{T}\bar{\text{T}}$-deformed Conformal Field Theories
• Holography and Irrelevant Operators
• TsT, black holes, and $T\bar{T}+J\bar{T}+T\bar{J}$
• S-duality in $T\bar{T}$-deformed CFT
• Topological Gauging and Double Current Deformations
• Infinite $\mathrm{T}\bar{\mathrm{T}}$-like symmetries of compactified LST
• On the universal behavior of $T\bar{T}$-deformed CFTs: single and double-trace partition functions at large $c$
• States, symmetries and correlators of $T\bar{T}$ and $J\bar{T}$ symmetric orbifolds
• Classical and quantum symmetries of $T\bar{T}$-deformed CFTs
• The Algebra of Diffeomorphisms from the World Sheet

Cited by in corpus (1)

• The on-shell action of supergravity & the B-side of TsT and single-trace $T\bar{T}$