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On Current-Squared Flows and ModMax Theories

by Christian Ferko, Liam Smith, Gabriele Tartaglino-Mazzucchelli

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Submission summary

Authors (as registered SciPost users): Christian Ferko
Submission information
Preprint Link:  (pdf)
Date accepted: 2022-07-12
Date submitted: 2022-07-05 04:42
Submitted by: Ferko, Christian
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • High-Energy Physics - Theory
Approach: Theoretical


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.

Published as SciPost Phys. 13, 012 (2022)

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