$T\bar T$-deformed Fermionic Theories Revisited

• URL: http://arxiv.org/abs/2104.09529v2
• Date: Fri, 9 Jul 2021 02:07:45 GMT
• Title: $T\bar T$-deformed Fermionic Theories Revisited
• Authors: Kyung-Sun Lee, Piljin Yi and Junggi Yoon
• Abstract summary: We revisit $Tbar T$ deformations of $d=2$ theories with fermions with a view toward the quantization. We ask about different $Tbar T$ deformations, such as manifestly supersymmetric $Tbar T$ and also more generally via the symmetric energy-momentum.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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