| ABSTRACT |
We revisit TT 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 TT 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 TT deformation of a N = (1, 1) theory from the latter, based on the Noether energy-momentum. This world- sheet 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 TT deformations, such as manifestly supersymmetric TT 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. |
