$T\bar T$-deformed Fermionic Theories Revisited

TL;DR

This paper investigates $T\bar T$ deformations of two-dimensional fermionic theories, analyzing their quantization, supersymmetry properties, and the implications of different deformation choices on degrees of freedom and unitarity.

Contribution

It provides a detailed analysis of $T\bar T$ deformations in fermionic theories, including explicit construction of supercharges and exploration of supersymmetric deformations and their effects.

Findings

Computed deformed Dirac brackets for Majorana doublets.

Identified hidden supercharges in certain $T\bar T$-deformed models.

Discovered potential unitarity issues and degree-of-freedom doubling in supersymmetric deformations.

Abstract

We revisit $T\bar T$ deformations of $d=2$ theories with fermions with a view toward the quantization. As a simple illustration, we compute the deformed Dirac bracket for a Majorana doublet and confirm the known eigenvalue flows perturbatively. We mostly consider those $T\bar T$ theories that can be reconstructed from string-like theories upon integrating out the worldsheet metric. After a quick overview of how this works when we add NSR-like or GS-like fermions, we obtain a known non-supersymmetric $T\bar T$ deformation of a $\cN=(1,1)$ theory from the latter, based on the Noether energy-momentum. This worldsheet reconstruction implies that the latter is actually a supersymmetric subsector of a $d=3$ GS-like model, implying hidden supercharges, which we do construct explicitly. This brings us to ask about different $T\bar T$ deformations, such as manifestly supersymmetric $T\bar T$ and also more generally via the symmetric energy-momentum. We show that, for theories with fermions, such choices often lead us to doubling of degrees of freedom, with potential unitarity issues. We show that the extra sector develops a divergent gap in the "small deformation" limit and decouples in the infrared, although it remains uncertain in what sense these can be considered a deformation.