Anti-symmetric Tensor Matter Fields and Non-Linear Sigma-Model

TL;DR

This paper explores the coupling of anti-symmetric tensor matter fields with Yang-Mills fields via non-linear sigma-models, revealing that matter becomes composite and highlighting potential phenomenological applications in meson interactions.

Contribution

It demonstrates the possibility of coupling tensor matter fields with gauge fields through sigma-model isometries, showing matter becomes composite and linking geometry to meson phenomenology.

Findings

Matter fields become composite in the coupled model.

Coupling is possible via gauging sigma-model isometries.

Applications include modeling vector meson interactions.

Abstract

The equivalence between rank-2 anti-symmetric tensor fields, considered as gauge potentials, and torsionless non-linear $\sigma$-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 $\sigma$-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 $\sigma$-model's target manifold is non-symmetric.