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

On p-form gauge theories and their conformal limits