Anti-symmetric tensor matter fields and non-linear σ-model

The equivalence between rank-2 anti-symmetric tensor fields, considered as gauge potentials, and torsionless non-linear σ-models suggests us to study the possibility of coupling tensorial matter with Yang-Mills fields, thorough the gauging of the isometries of the target space. We show that this coupling is actually possible; however the matter appears no longer as an elementary field, but rather as a composite one, expressed in terms of the bosonic degrees of freedom of the σ-model. A possible phenomenological application is presented that describes the interactions among vector mesons in terms of the geometrical properties of the target manifold. Also, spin-2 meson resonances may naturally be accommodated whenever the σ-model's target manifold is non-symmetric. (author)