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 by a quadratic combi-nation of stress-energy tensors. The operator associated to this flow is a 4d analogue of the T 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 N = 1 supersymmetric version of the ModMax-Born-Infeld theory obeys a related supercurrent-squared flow which is formulated directly in N = 1 superspace.

Automated summary

This paper investigates the relationship between the ModMax theory and its Born-Infeld-like generalization in electrodynamics, and reveals that they are connected by a flow equation driven by a quadratic combination of stress-energy tensors. It is shown that this result generalizes the relationship between the ordinary Born-Infeld Lagrangian and the free Maxwell theory, and it is demonstrated that no similar relationship exists in dimensions other than four. Additionally, the N = 1 supersymmetric version of the ModMax-Born-Infeld theory is found to obey a related supercurrent-squared flow formulated directly in N = 1 superspace.