Twisted BRST symmetry in gauge theories on $\kappa$-Minkowski

TL;DR

This paper explores the algebraic structure of twisted BRST symmetry in gauge theories on $ppa$-Minkowski space, revealing a noncommutative analog of the Yang-Mills BRST algebra through deformation and twisting.

Contribution

It demonstrates how the BRST operation in $ppa$-Minkowski gauge theories can be deformed into a nilpotent twisted BRST operation, establishing a noncommutative BRST algebra.

Findings

The twisted BRST operation can be continuously deformed into a nilpotent form.

The resulting twisted BRST algebra generalizes the usual Yang-Mills BRST algebra to noncommutative geometry.

The algebraic properties of gauge invariance are preserved under this deformation.

Abstract

Algebraic properties of the BRST symmetry associated to the twisted gauge symmetry occurring in the $\kappa$-Poincar\'e invariant gauge theories on the $\kappa$-Minkowski space are investigated. We find that the BRST operation associated to the gauge invariance of the action functional can be continuously deformed together with its corresponding Leibniz rule, into a nilpotent twisted BRST operation, leading to a twisted BRST symmetry algebra which may be viewed as a noncommutative analog of the usual Yang-Mills BRST algebra.