$T\overline{T}$ deformation in SCFTs and integrable supersymmetric theories

TL;DR

This paper investigates the effects of $T\overline{T}$ deformation on 2D superconformal field theories, calculating deformed multiplets, correlators, and ground state energies, and finds certain indices remain invariant under the deformation.

Contribution

It provides the first calculation of $T\overline{T}$ deformed multiplets and correlators in 2D supersymmetric SCFTs, and analyzes the deformation's impact on integrable models and topological indices.

Findings

Deformed multiplets and correlators are explicitly computed.

Ground state energy obeys the inviscid Burgers' equation under deformation.

Indices like the Witten index remain invariant under $T\overline{T}$ deformation.

Abstract

We calculate the $\mathcal{S}$-multiplets for two-dimensional Euclidean $\mathcal{N}=(0,2)$ and $\mathcal{N} = (2,2)$ superconformal field theories under the $T\overline{T}$ deformation at leading order of perturbation theory in the deformation coupling. Then, from these $\mathcal{N} = (0, 2)$ deformed multiplets, we calculate two- and three-point correlators. We show the $\mathcal{N} = (0,2)$ chiral ring's elements do not flow under the $T\overline{T}$ deformation. Specializing to integrable supersymmetric seed theories, such as $\mathcal{N} = (2,2)$ Landau-Ginzburg models, we use the thermodynamic Bethe ansatz to study the S-matrices and ground state energies. From both an S-matrix perspective and Melzer's folding prescription, we show that the deformed ground state energy obeys the inviscid Burgers' equation. Finally, we show that several indices independent of $D$-term perturbations including the Witten index, Cecotti-Fendley-Intriligator-Vafa index and elliptic genus do not flow under the $T\overline{T}$ deformation.