We revisit \( T\overline{T} \) 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 \( T\overline{T} \) 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 \( T\overline{T} \) deformation of a \( \mathcal{N} \) = (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 \( T\overline{T} \) deformations, such as manifestly supersymmetric \( T\overline{T} \) 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.

我们用费米子重新审视d = 2 理论的\( T\overline{T} \)变形，以实现量化。作为一个简单的说明，我们计算马约拉纳双峰的变形狄拉克括号并确认已知的特征值流。我们主要考虑那些\( T\overline{T} \)理论，这些理论可以通过整合世界表度量从类弦理论重建。在我们快速了解当我们添加类 NSR 或类 GS 费米子时这是如何工作的之后，我们获得了一个已知的非超对称\( T\overline{T} \)变形\( \mathcal{N} \) = (1 ,1) 后者的理论，基于诺特能量动量。这个世界表重建意味着后者实际上是d = 3 类 GS 模型的超对称子扇区，暗示隐藏的增压，我们确实明确构建了它。这让我们要问不同的\( T\overline{T} \)变形，例如明显超对称\( T\overline{T} \)并且更普遍地通过对称能量动量。我们表明，对于有费米子的理论，这样的选择通常会导致我们的自由度加倍，并存在潜在的幺正性问题。我们表明，额外的扇区在“小变形”极限中形成了发散间隙，并在红外线中解耦，尽管在何种意义上这些可以被视为变形仍然不确定。