$$ T\overline{T} $$ deformed CFT as a non-critical string

Abstract

We present a new exact treatment of TT deformed 2D CFT in terms of the worldsheet theory of a non-critical string. The transverse dimensions of the non-critical string are represented by the undeformed CFT, while the two longitudinal light-cone directions are described by two scalar fields X + and X − with free field OPE's but with a modified stress tensor, arranged so that the total central charge adds up to 26. The relation between our X ± field variables and 2D dilaton gravity is indicated. We compute the physical spectrum and the partition function and find a match with known results. We describe how to compute general correlation functions and present an integral expression for the three point function, which can be viewed as an exact formula for the OPE coefficients of the TT deformed theory. We comment on the relationship with other proposed definitions of local operators.

Hamiltonian deformations in quantum mechanics, TT¯ , and the SYK model

“…The closed worldline thus becomes an open one with "boundary" states jX 1 i and jX 2 i at its ends. This is similar to the D-brane boundary condition proposed for TT deformed 2d conformal field theory (CFTs) in [28]. The path integral we then wish to compute is a transition amplitude:…”

“…By coupling the undeformed theory to a theory of one-dimensional gravity and performing the path integral over all fields, we showed that the thermal partition function is precisely reproduced. This is analogous to the description of the TT deformation of two-dimensional theories as coupling to JT gravity or 2d non-critical string theory [26][27][28].…”

TsT, $$ \mathrm{T}\overline{\mathrm{T}} $$ and black strings

“…These include the TT deformations and their higher-spin generalizations [57][58][59], the JT /TJ deformations in theories with a conserved U(1) current [60,61], and their linear combinations [62][63][64]. These deformations enjoy remarkable properties including closed formulae for the deformed spectrum, modular invariance (TT ) or covariance (JT /TJ) of the torus partition functions [65][66][67][68][69], as well as connections to strings and 2d gravity [59,[70][71][72][73][74][75][76][77][78]. The holographic interpretation of these irrelevant deformations include the double-trace version which changes the boundary conditions but does not change the local bulk geometry [79][80][81], as well as a single-trace version which also changes the local geome-…”

Chiral decoupling from irrelevant deformations

“…Since our analyses in this note are purely based on equation of motion, it is possible that this chiral decoupling doesn't persist when quantum corrections are considered. It would be interesting to study the corresponding quantum field theories, perhaps along the lines of [9,35]. We hope to return to these questions in the near future.…”