Characters of irrelevant deformations

TL;DR

This paper derives explicit formulas for how $T\bar{T}$ and related irrelevant deformations affect 2D CFT characters on the torus, revealing state-dependent coordinate changes and implications for holography.

Contribution

It provides closed-form expressions for deformed CFT characters in a large central charge limit, including generalizations to multiple deformations.

Findings

Deformation formulas resemble CFT structure with rescaled modular parameters

State-dependent coordinate transformations emerge from deformations

Results inform holographic models of irrelevant deformations

Abstract

We analyse the $T\bar{T}$ deformation of 2d CFTs in a special double-scaling limit, of large central charge and small deformation parameter. In particular, we derive closed formulae for the deformation of the product of left and right moving CFT characters on the torus. It is shown that the $1/c$ contribution takes the same form as that of a CFT, but with rescalings of the modular parameter reflecting a state-dependent change of coordinates. We also extend the analysis for more general deformations that involve $T\bar{T}$, $J\bar{T}$ and $T\bar{J}$ simultaneously. We comment on the implications of our results for holographic proposals of irrelevant deformations.