Stress Tensor flows, birefringence in non-linear electrodynamics and supersymmetry

We identify the unique stress tensor deformation which preserves zero-birefringence conditions in non-linear electrodynamics, which is a 4d version of the T T operator. We study the flows driven by this operator in the three Lagrangian theories without birefringence - Born-Infeld, Plebanski, and reverse Born-Infeld - all of which admit ModMax-like generalizations using a root -T T-like flow that we analyse in our paper. We demonstrate one way of making this root -TT-like flow manifestly supersymmetric by writing the deforming operator in N = 1 superspace and exhibit two examples of superspace flows. We present scalar analogues in d = 2 with similar properties as these theories of electrodynamics in d = 4. Surprisingly, the Plebanski-type theories are fixed points of the classical TT-like flows, while the Born-Infeld-type examples satisfy new flow equations driven by relevant operators constructed from the stress tensor. Finally, we prove that any theory obtained from a classical stress-tensor-squared deformation of a conformal field theory gives rise to a related "subtracted" theory for which the stress-tensor-squared operator is a constant.