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

Abstract

Abstract We define a manifestly supersymmetric version of the $$ T\overline{T} $$ T T ¯ deformation appropriate for a class of (0 + 1)-dimensional theories with $$ \mathcal{N} $$ N = 1 or $$ \mathcal{N} $$ N = 2 supersymmetry, including one presentation of the super-Schwarzian theory which is dual to JT supergravity. These deformations are written in terms of Noether currents associated with translations in superspace, so we refer to them collectively as f($$ \mathcal{Q} $$ Q ) deformations. We provide evidence that the f($$ \mathcal{Q} $$ Q )) deformations of $$ \mathcal{N} $$ N = 1 and $$ \mathcal{N} $$ N = 2 theories are on-shell equivalent to the dimensionally reduced supercurrent-squared deformations of 2d theories with $$ \mathcal{N} $$ N = (0, 1) and $$ \mathcal{N} $$ N = (1, 1) supersymmetry, respectively. In the $$ \mathcal{N} $$ N = 1 case, we present two forms of the f($$ \mathcal{Q} $$ Q ) deformation which drive the same flow, and clarify their equivalence by studying the analogous equivalent deformations in the non-supersymmetric setting.