Novel generalization of three-dimensional Yang–Mills theory

Abstract

A class of new non-Abelian gauge theories for vector fields on three manifolds is presented. The theories describe a generalization of three-dimensional Yang–Mills theory featuring a novel nonlinear gauge symmetry and field equations for Lie-algebra-valued vector potential fields. The nonlinear form of the gauge symmetry and field equations relies on the vector cross-product and vector curl operator available only in three dimensions, and makes use of an auxiliary Lie bracket together with the Lie bracket used in Yang–Mills theory. A gauge covariant formulation of the new theories is given which utilizes the covariant derivative and curvature from the geometrical formulation of Yang–Mills theory. Further features of the new theories are discussed.