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-2/2-forms. Denoting by e(Lambda)(I) and m(ILambda) the electric and magnetic couplings, gauge invariance requires: e(Lambda)(I) m(JLambda) -/+ e(Lambda)(J) m(ILambda) = 0, where I, Lambda = 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, Lambda = 1 for D = 4n and I, Lambda = 1, 2 for D = 4n + 2) both the e, m quantum numbers contribute to the mass mu = roote(2) + m(2). 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. (C) 2004 Elsevier B.V. All rights reserved.