Massive Gauge Axion Fields

A gauge invariant formulation for the massive axion is considered. The axion acquires mass through a topological term which couples a (pseudo)scalar and a third rank antisymmetric tensor. Duality, local and canonical equivalences with the non-gauge invariant proposal are established. The supersymmetric version of the gauge invariant model is constructed. It is well known that different theories can be related by duality transformations and their classical and quantum properties are equivalent. In four dimensions a massless (pseudo)scalar field: the axion, is dual to the antisymmetric field Bmn (only if derivative couplings are considered). This fact is a particular case of the general duality between p and D − p − 2 forms in D dimensions. In this sense, it is known that non-perturbative effects break the Pecci-Quinn (PQ) symmetry of the axion, giving mass to it. Then, a natural question arises, concernig about what happens with the duality symmetry. This item was an enigma until two independent approaches were developed recently [1], [2]. In these references the authors show that, though the PQ symmetry is broken, duality symmetry still remains. The Bmn field is replaced by a massive antisymmetric field of third rank Cmnp. A characteristic feature of this duality is the lost of abelian gauge invariance for the new antisymmetric field. The duality now corresponds to a particular case of the usual duality between massive p and D − p− 1 forms in D dimensions. The conection between a massive (pseudo)scalar field, φ, and a massive antisymmetric field, Cmnp has been considered before in different contexts