Dyonic masses from conformal field strengths in D even dimensions

We show that D/2-form gauge fields in D even dimensions can get a mass with both electric and magnetic contributions when coupled to conformal field-strengths whose gauge potentials are D−22-forms. Denoting by eΛI and mIΛ the electric and magnetic couplings, gauge invariance requires: eΛImJΛ∓eΛJmIΛ=0, where I,Λ=1,…,m denote the species of gauge potentials of degree D/2 and gauge fields of degree D/2−1, respectively. The minus and plus signs refer to the two different cases D=4n and D=4n+2, respectively, and the given constraints are respectively Sp(2m) and O(m,m) invariant. For the simplest examples (I,Λ=1 for D=4n and I,Λ=1,2 for D=4n+2) both the e,m quantum numbers contribute to the mass μ=e2+m2. This phenomenon generalizes to D even dimensions the coupling of massive antisymmetric tensors which appear in D=4 supergravity Lagrangians, which derive from flux compactifications in higher dimensions. For D=4 we give the supersymmetric generalization of such couplings using N=1 superspace.