Gauge theory deformations and novel Yang-Mills Chern-Simons field theories with torsion

TL;DR

This paper develops a universal geometric framework for classifying nonlinear gauge theory deformations, introduces a novel Yang-Mills generalization with torsion in three dimensions, and explores their geometric and field-theoretic properties.

Contribution

It uncovers a universal geometric structure for nonlinear gauge theories and proposes a new Yang-Mills extension with torsion derived from deformation analysis.

Findings

Identified a common geometric structure in various nonlinear gauge theories.

Derived a new 3D Yang-Mills generalization incorporating torsion.

Discussed the geometric and field-theoretic features of the torsion-inclusive theories.

Abstract

A basic problem of classical field theory, which has attracted growing attention over the past decade, is to find and classify all nonlinear deformations of linear abelian gauge theories. The first part of this paper summarizes and significantly elaborates a field- theoretic deformation method developed in earlier work. As a key contribution presented here, a universal geometrical structure common to a large class of nonlinear gauge theory examples is uncovered. This structure is derived geometrically from the deformed gauge symmetry and is characterized by a covariant derivative operator plus a nonlinear field strength, related through the curvature of the covariant derivative. The scope of these results encompasses Yang-Mills theory, Freedman-Townsend theory, Einstein gravity theory, in addition to their many interesting types of novel generalizations that have been found in the past several years. The second part of the paper presents a new geometrical type of Yang-Mills generalization in three dimensions motivated from considering torsion in the context of nonlinear sigma models with Lie group targets (chiral theories). The generalization is derived by a deformation analysis of linear abelian Yang-Mills Chern-Simons gauge theory. Torsion is introduced geometrically through a duality with chiral models obtained from the chiral field form of self-dual 2+2 dimensional Yang-Mills theory under reduction to 2+1 dimensions. Field-theoretic and geometric features of the resulting nonlinear gauge theories with torsion are discussed.