Nonabelian Topological Mass Generation in 4 Dimensions

TL;DR

This paper extends topological mass generation mechanisms from abelian to nonabelian gauge theories in four dimensions, introducing auxiliary fields and BRST symmetry to achieve gauge-invariant mass terms.

Contribution

It develops a nonabelian gauge invariant action with topological mass generation, including auxiliary fields and BRST symmetry, extending previous abelian results.

Findings

Massive gauge fields via topological coupling in nonabelian theories

Construction of BRST/anti-BRST invariant quantum action

Extension of abelian topological mass generation to nonabelian case

Abstract

We study the topological mass generation in the 4 dimensional nonabelian gauge theory, which is the extension of the Allen $et$ $al.$'s work in the abelian theory. It is crucial to introduce a one form auxiliary field in constructing the gauge invariant nonabelian action which contains both the one form vector gauge field $A$ and the two form antisymmetric tensor field $B$. As in the abelian case, the topological coupling $m B\wedge F$, where $F$ is the field strength of $A$, makes the transmutation among $A$ and $B$ possible, and consequently we see that the gauge field becomes massive. We find the BRST/anti-BRST transformation rule using the horizontality condition, and construct a BRST/anti-BRST invariant quantum action.