Genus Two Correlation Functions in CFTs with $T\bar{T}$ Deformation

TL;DR

This paper develops a method to compute the first-order $Tar{T}$ deformation effects on correlation functions in conformal field theories on genus two Riemann surfaces using sewing techniques and perturbative approaches.

Contribution

It introduces a novel sewing-based approach to define and compute $Tar{T}$ deformations on higher genus surfaces, extending previous methods to genus two.

Findings

First-order $Tar{T}$ correction to genus two correlation functions obtained

Method applicable to partition functions and multi-point correlators

Provides a systematic way to study deformations on complex Riemann surfaces

Abstract

Since the definition of $T\bar{T}$ deformation in the curved Riemann surface is obstructive in the literature, we propose a way to do the deformation in the genus two Riemann surfaces by sewing prescription. We construct the correlation functions of conformal field theories (CFTs) on genus two Riemann surfaces with the $T\bar{T}$ deformation in terms of the perturbative CFT approach. Thanks to sewing construction to form higher genus Riemann surfaces from lower genus ones and conformal symmetry, we systematically obtain the first order $T\bar{T}$ correction to the genus two correlation functions in the $T\bar{T}$ deformed CFTs, e.g., partition function and one/higher-point correlation functions.