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

Abstract

Abstract We define a manifestly supersymmetric version of the T T ¯ $$ T\overline{T} $$ deformation appropriate for a class of (0 + 1)-dimensional theories with N $$ \mathcal{N} $$ = 1 or N $$ \mathcal{N} $$ = 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( Q $$ \mathcal{Q} $$ ) deformations. We provide evidence that the f( Q $$ \mathcal{Q} $$ )) deformations of N $$ \mathcal{N} $$ = 1 and N $$ \mathcal{N} $$ = 2 theories are on-shell equivalent to the dimensionally reduced supercurrent-squared deformations of 2d theories with N $$ \mathcal{N} $$ = (0, 1) and N $$ \mathcal{N} $$ = (1, 1) supersymmetry, respectively. In the N $$ \mathcal{N} $$ = 1 case, we present two forms of the f( Q $$ \mathcal{Q} $$ ) deformation which drive the same flow, and clarify their equivalence by studying the analogous equivalent deformations in the non-supersymmetric setting.

Keywords

• Field Theories in Lower Dimensions
• Superspaces
• Extended Supersymmetry