The correlation function of (1,1) and (2,2) supersymmetric theories with $T\bar{T}$ deformation

TL;DR

This paper investigates how $Tar{T}$ deformation affects correlation functions in 2D supersymmetric conformal field theories, extending previous bosonic results to supersymmetric cases using perturbation theory and Ward identities.

Contribution

It provides the first perturbative computation of $Tar{T}$-deformed correlation functions in $ abla=(1,1)$ and $ abla=(2,2)$ supersymmetric theories, utilizing superconformal Ward identities.

Findings

Correlation functions are computed at leading order in deformation.

Superconformal Ward identities facilitate the calculation of deformed correlators.

Dimensional regularization is used to evaluate integrals in the perturbative expansion.

Abstract

In the paper, based on recent studies on $T\bar{T}$ deformation of 2D field theory with supersymmetry, we investigate the deformed correlation functions in $\mathcal{N}=(1,1)$ and $\mathcal{N}=(2,2)$ 2D superconformal field theories. Up to the leading order in perturbation theory, we compute the correlation functions under $T\bar{T}$ deformation. The correlation functions in these undeformed theories are almost known, and together with the help of superconformal Ward identity in $\mathcal{N}=(1,1)$ and $\mathcal{N}=(2,2)$ theories respectively we can obtain the correlation functions with operator $T\bar{T}$ inserted. Finally, by employing dimensional regularization, we can work out the integrals in the first order perturbation. The study in this paper extends previous works on the correlation functions of $T\bar{T}$ deformed bosonic CFT to the supersymmetric case.