Duality-Invariant Non-linear Electrodynamics and Stress Tensor Flows

TL;DR

This paper proves that duality-invariant non-linear electrodynamics theories are connected through stress tensor flows, providing new insights into their structure and auxiliary field representations.

Contribution

It establishes a novel relation between duality-invariant Lagrangians and stress tensor flows, and introduces a new auxiliary field formulation for ModMax-Born-Infeld theories.

Findings

Stress tensor deformations preserve duality invariance.

Any duality-invariant Lagrangian family is related by stress tensor flows.

New auxiliary field representation for ModMax-Born-Infeld theories.

Abstract

Given a model for self-dual non-linear electrodynamics in four spacetime dimensions, any deformation of this theory which is constructed from the duality-invariant energy-momentum tensor preserves duality invariance. In this work we present new proofs of this known result, and also establish a previously unknown converse: any parameterized family of duality-invariant Lagrangians, all constructed from an Abelian field strength $F_{\mu \nu}$ but not its derivatives, is related by a generalized stress tensor flow, in a sense which we make precise. We establish this and other properties of stress tensor deformations of theories of non-linear electrodynamics using both a conventional Lagrangian representation and using two auxiliary field formulations. We analyze these flows in several examples of duality-invariant models including the Born-Infeld and ModMax theories, and we derive a new auxiliary field representation for the two-parameter family of ModMax-Born-Infeld theories. These results suggest that the space of duality-invariant theories may be characterized as a subspace of theories of electrodynamics with the property that all tangent vectors to this subspace are operators constructed from the stress tensor.