On p-form gauge theories and their conformal limits

TL;DR

This work identifies a universal PDE framework that ties together Lorentz-invariant duality-invariant (4D) electrodynamics and Lorentz-invariant chiral (6D) 2-form electrodynamics, revealing a one-to-one correspondence between 4D duality-symmetric theories and 6D chiral theories via dimensional reduction. It introduces a one-parameter ModMax generalization in 4D and a new 6D chiral-2-form family whose weak-field limits map to ModMax upon reduction, with strong-field limits yielding BB- or SL(2;R)-duality-invariant structures. The results generalize to higher dimensions: in $D=4n$ one has generalized BI-type theories for $(2n-1)$-forms, and in $D=4n+2$ a conformal chiral $(2n)$-form theory reduces to a duality-invariant $(2n-1)$-form theory in $D=4n$, though the reduction does not always reproduce all higher-dimensional BB-type models. Collectively, these findings illuminate the intricate web linking duality, chirality, conformal invariance, and dimensional reduction across dimensions, and they establish the D3/M5 pair as part of a broader, highly structured spectrum of coupled 4D/6D theories with potential implications for string/M-theory brane dynamics.

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.