On Current-Squared Flows and ModMax Theories

TL;DR

This paper establishes a flow equation connecting ModMax electrodynamics and its Born-Infeld-like extension via stress-energy tensor combinations, highlighting a unique four-dimensional relationship similar to the 2D $T\bar{T}$ deformation.

Contribution

It introduces a flow equation linking ModMax and Born-Infeld theories through stress-energy tensors, extending the $T\bar{T}$ deformation concept to four dimensions and supersymmetric cases.

Findings

ModMax and Born-Infeld theories are related by a stress-energy tensor flow in 4D.

No similar relationship exists in dimensions other than four.

Supersymmetric ModMax-Born-Infeld obeys a supercurrent-squared flow in superspace.

Abstract

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