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

Abstract

We calculate the $$ \mathcal{S} $$ S -multiplets for two-dimensional Euclidean $$ \mathcal{N} $$ N = (0, 2) and $$ \mathcal{N} $$ N = (2, 2) superconformal field theories under the T$$ \overline{T} $$ T ¯ deformation at leading order of perturbation theory in the deformation coupling. Then, from these $$ \mathcal{N} $$ N = (0, 2) deformed multiplets, we calculate two- and three-point correlators. We show the $$ \mathcal{N} $$ N = (0, 2) chiral ring’s elements do not flow under the T$$ \overline{T} $$ T ¯ deformation. Specializing to integrable supersymmetric seed theories, such as $$ \mathcal{N} $$ 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$$ \overline{T} $$ T ¯ deformation.

$$ T\overline{T} $$ deformations of supersymmetric quantum mechanics

“…Other quantities in the deformed theory -such as the torus partition function [36][37][38], the flat space S-matrix [39,40], torus one-point functions [41], and (to some degree) correlation functions [42][43][44][45][46][47][48][49][50][51][52] -can also be related to quantities in the undeformed theory. One interesting consequence of these results is that the high-energy density of states in a T Tdeformed theory follows Hagedorn rather than Cardy growth, which means that it cannot be a local quantum field theory and instead shares some properties with string theories.…”

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

“…( 12), T T (z, z) is regular on the annulus A, and its integral over A vanishes under condition eq. (34). Finally, the first-order deformation of the partition function can be divided into two parts…”

“…The correlation functions for stress tensor operators have been obtained in terms of random geometry [27,28] and holography [29][30][31][32]. The deformed correlation functions for generic operators have been obtained in perturbative CFT approach [20,21,33,34]. In [35], they obtained the deformed correlation functions of the deep UV theories in a nonperturbative way.…”

Supersymmetric black holes and $T\bar T$ deformation

“…Change of degeneracies?-It has been argued that the degeneracies are not lifted under the T T deformation [24], and similarly that supersymmetric indices remain unchanged [69]. This suggests that the Ω(γ; t ∞ γ ) remain the same as function of γ.…”