On p-form gauge theories and their conformal limits

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; )-duality invariant theory of (2n - 1)-form electrodynamics.

Automated summary

This paper clarifies the relationships between various formulations of nonlinear p-form electrodynamics, focusing on the duality invariant (2n - 1)-form electrodynamics and chiral 2n-form electrodynamics. It introduces a new family of chiral 2-form electrodynamics in D = 6 and shows the dimensional reduction relationship between weak-field limits and the ModMax generalization of Maxwell's equations. Additionally, it demonstrates the dimensional reduction of chiral 'strong-field' 2n-form electrodynamics to a new Sl(2; )-duality invariant theory of (2n - 1)-form electrodynamics for n > 1.