Dyonic Masses from Conformal Field Strengths in D even Dimensions

TL;DR

This paper demonstrates how D/2--form gauge fields in even dimensions can acquire mass through electric and magnetic couplings, with gauge invariance imposing specific constraints, generalizing known antisymmetric tensor couplings in supergravity.

Contribution

It introduces a new mechanism for mass generation of gauge fields in even dimensions via conformal field strengths, extending previous supergravity results to higher dimensions.

Findings

Mass of gauge fields depends on electric and magnetic couplings as =

Gauge invariance imposes symplectic or orthogonal constraints on couplings

Mass formula = applies to simple cases and generalizes known supergravity couplings

Abstract

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 is are \frac {D-2}{2}- forms. Denoting by e^I_\L and m^{I\L} the electric and magnetic couplings, gauge invariance requires: e^I_\L m^{J\L}\mp e^J_\L m^{I\L}=0, where I,\L= 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 {\rm {Sp}}(2m) and {\rm {O}}(m,m) invariant. For the simplest examples, (I,\L=1 for D=4n and I,\L=1,2 for D=4n+2) both the e,m quantum numbers contribute to the mass \m=\sqrt {e^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.