Local BRST cohomology in the antifield formalism: II. Application to Yang-Mills theory

TL;DR

This paper applies advanced cohomological methods to Yang-Mills theories to classify local BRST cohomology, revealing new solutions at higher ghost numbers and confirming known solutions at lower ghost numbers.

Contribution

It extends the local BRST cohomology analysis to Yang-Mills models with matter, identifying new solutions depending on antifields at ghost number two or higher.

Findings

New solutions to $sa+db=0$ depending on antifields at ghost number ≥ 2

At ghost number 0 or 1, no new solutions from antifields

Method is purely cohomological and adaptable to more general actions

Abstract

Yang-Mills models with compact gauge group coupled to matter fields are considered. The general tools developed in a companion paper are applied to compute the local cohomology of the BRST differential $s$ modulo the exterior spacetime derivative $d$ for all values of the ghost number, in the space of polynomials in the fields, the ghosts, the antifields (=sources for the BRST variations) and their derivatives. New solutions to the consistency conditions $sa+db=0$ depending non trivially on the antifields are exhibited. For a semi-simple gauge group, however, these new solutions arise only at ghost number two or higher. Thus at ghost number zero or one, the inclusion of the antifields does not bring in new solutions to the consistency condition $sa+db=0$ besides the already known ones. The analysis does not use power counting and is purely cohomological. It can be easily extended to more general actions containing higher derivatives of the curvature, or Chern-Simons terms.