2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/55623The 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, through 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.9 pages, LatexHigh Energy Physics - Theorytext