On Current-Squared Flows and ModMax Theories

We show that the recently introduced ModMax theory of electrodynamics and its Born-Infeld-like generalization are related by a flow equation driven quadratic combination stress-energy tensors. The operator associated to this is $4d$ analogue $T\bar{T}$ deformation in two dimensions. This result generalizes observation ordinary Born-Infeld Lagrangian free Maxwell current-squared flow. As case, we no analogous relationship holds any other dimension besides $d=4$. also demonstrate $\mathcal{N}=1$ supersymmetric version ModMax-Born-Infeld obeys supercurrent-squared which formulated directly superspace.