States, symmetries and correlators of $T\bar{T}$ and $ J\bar{T} $ symmetric orbifolds

TL;DR

This paper investigates the properties of symmetric orbifolds of $T\bar{T}$ and $J\bar{T}$-deformed CFTs, deriving partition functions, symmetry preservation, and correlation functions using Hilbert space methods without relying on conformal invariance.

Contribution

It generalizes the torus partition function formula to non-conformal QFTs and shows symmetry preservation in single-trace deformations, extending correlation function computations to twisted sectors.

Findings

Partition function formula extended to non-conformal theories.

Virasoro and Kac-Moody symmetries preserved under deformations.

Explicit correlation functions computed for untwisted and twisted sectors.

Abstract

We derive various properties of symmetric product orbifolds of $T\bar{T}$ and $J\bar{T}$ - deformed CFTs from a field-theoretical perspective. First, we generalise the known formula for the torus partition function of a symmetric orbifold theory in terms of the one of the seed to non-conformal two-dimensional QFTs; specialising this to seed $T\bar{T}$ and $J\bar{T}$ - deformed CFTs reproduces previous results in the literature. Second, we show that the single-trace $T\bar{T}$ and $J\bar{T}$ deformations preserve the Virasoro and Kac-Moody symmetries of the undeformed symmetric product orbifold CFT, including their fractional counterparts, as well as the KdV charges. Finally, we discuss correlation functions in these theories. By extending a previously-proposed basis of operators for $J\bar{T}$ - deformed CFTs to the single-trace case, we explicitly compute the correlation functions of both untwisted and twisted-sector operators and compare them to an appropriate set of holographic correlators. Our derivations are based mainly on Hilbert space techniques and completely avoid the use of conformal invariance, which is not present in these models.