On p-form gauge theories and their conformal limits

A bstract 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 (2 n − 1)-form electrodynamics and chiral 2 n -form electrodynamics in Minkowski spacetime of dimension D = 4 n and D = 4 n + 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’ 2 n -form electrodynamics is related by dimensional reduction to a new Sl (2; ℝ)-duality invariant theory of (2 n − 1)-form electrodynamics.