Antisymmetric tensor gauge theories and non-linear σ-models

Abstract

Antisymmetric tensor fields B μν subject to the gauge transformation δB μν = ϖ μ ξ ν − ϖ ν ξ μ can describe spinless particles. We investigate the properties of field theories with a “non-abelian generalization” of this invariance. One class of such theories is equivalent to non-linear principal chiral σ-models, another to massive Yang-Mills theories. A supersymmetric analogue in 2 + 2 superspace is constructed and leads to the supersymmetric σ-model defined on a general riemannian manifold.