T(T)over-bar deformations of supersymmetric quantum mechanics

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

Automated summary

This work introduces a manifestly supersymmetric version of the T(bar)T deformation suitable for (0 + 1)-dimensional theories with N = 1 or N = 2 supersymmetry and presents the corresponding f(Q) deformations. Evidence is provided showing the on-shell equivalence between the f(Q) deformations of N = 1 and N = 2 theories and the dimensionally reduced supercurrent-squared deformations of 2d theories with different levels of supersymmetry. Additionally, two forms of the f(Q) deformation in the N = 1 case are discussed and their equivalence is clarified through analogous deformations in the non-supersymmetric setting.