Topological mass generation in four-dimensional gauge theory

TL;DR

This paper introduces a gauge-invariant, metric-independent density in four-dimensional gauge theory that enables mass generation for Yang-Mills bosons without breaking gauge symmetry, extending to high-rank tensor bosons.

Contribution

It presents a novel four-dimensional Chern-Simons-like density that induces gauge-invariant mass terms for non-Abelian tensor gauge fields, advancing mass generation mechanisms in gauge theories.

Findings

Identified a four-dimensional analog of the Chern-Simons density.

Demonstrated gauge-invariant mass generation for Yang-Mills bosons.

Proposed invariant densities for high-rank tensor bosons.

Abstract

The Lagrangian of non-Abelian tensor gauge fields describes the interaction of the Yang-Mills and massless tensor bosons of increasing helicities. We have found a metric-independent gauge invariant density which is a four-dimensional analog of the Chern-Simons density. The Lagrangian augmented by this Chern-Simons-like invariant describes massive Yang-Mills boson, providing a gauge-invariant mass gap for a four-dimensional gauge field theory. We present invariant densities which can provide masses to the high rank tensor bosons.