Gauge theories of Yang–Mills vector fields coupled to antisymmetric tensor fields

Abstract

A non-Abelian class of massless/massive nonlinear gauge theories of Yang–Mills vector potentials coupled to Freedman–Townsend antisymmetric tensor potentials is constructed in four space–time dimensions. These theories involve an extended Freedman–Townsend-type coupling between the vector and tensor fields, and a Chern–Simons mass term with the addition of a Higgs-type coupling of the tensor fields to the vector fields in the massive case. Geometrical, field theoretic, and algebraic aspects of the theories are discussed in detail. In particular, the geometrical structure mixes and unifies features of Yang–Mills theory and Freedman–Townsend theory formulated in terms of Lie algebra valued curvatures and connections associated to the fields and nonlinear field strengths. The theories arise from a general determination of all possible geometrical nonlinear deformations of linear Abelian gauge theory for one-form fields and two-form fields with an Abelian Chern–Simons mass term in four dimensions. For this type of deformation (with typical assumptions on the allowed form considered for terms in the gauge symmetries and field equations), an explicit classification of deformation terms at first-order is obtained, and uniqueness of deformation terms at all higher orders is proven. This leads to a uniqueness result for the non-Abelian class of theories constructed here.