On p-form gauge theories and their conformal limits

TL;DR

This paper explores the relationships between various nonlinear p-form electrodynamics theories and their conformal limits, introducing new models and connections to duality invariance and recent Maxwell generalizations.

Contribution

It clarifies the links between different formulations of p-form electrodynamics and introduces new conformally invariant models, including a novel chiral 2-form theory in six dimensions.

Findings

Exhibits a new family of chiral 2-form electrodynamics in D=6.

Shows the weak-field limit relates to the ModMax generalization of Maxwell's equations.

Establishes a connection between strong-field chiral theories and Sl(2;R)-duality invariant models.

Abstract

Relations between the various formulations of nonlinear p-form electrodynamics with conformal-invariant weak-field and strong-field limits are clarified, with a focus on duality invariant (2n-1)-form electrodynamics and chiral 2n-form electrodynamics in Minkowski spacetime of dimension D=4n and D=4n+2, respectively. We exhibit a new family of chiral 2-form electrodynamics in D=6 for which these limits exhaust the possibilities for conformal invariance; the weak-field limit is related by dimensional reduction to the recently discovered ModMax generalisation of Maxwell's equations. For n>1 we show that the chiral `strong-field' 2n-form electrodynamics is related by dimensional reduction to a new Sl(2;R)-duality invariant theory of (2n-1)-form electrodynamics.