Novel generalization of three-dimensional Yang-Mills theory

TL;DR

This paper introduces a new class of three-dimensional nonabelian gauge theories that extend Yang-Mills theory by incorporating a novel nonlinear gauge symmetry based on vector calculus in three dimensions.

Contribution

It presents a generalized framework for 3D Yang-Mills theories with a unique nonlinear gauge symmetry involving vector cross-products and curls, expanding the theoretical landscape.

Findings

New nonlinear gauge symmetry based on vector calculus

Gauge covariant formulation using geometrical concepts

Discussion of additional features of the theories

Abstract

A class of new nonabelian 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.