Partial Gauge Fixing and Equivariant Cohomology

TL;DR

This paper explores partial gauge fixing in gauge theories, revealing the necessity of equivariant cohomology and quartic ghost terms, with applications in D-brane models, QCD, and grand unified theories.

Contribution

It systematically develops the algebraic and path integral framework for partial gauge fixing, introducing equivariant cohomology and quartic ghost terms as essential components.

Findings

Equivariant BRST cohomology replaces standard cohomology.

Quartic ghost terms are necessary at tree level.

Applications include models of emergent space and low-energy GUT theories.

Abstract

Given a gauge theory with gauge group G, it is sometimes useful to find an equivalent formulation in terms of a non-trivial gauge subgroup H of G. This amounts to fixing the gauge partially from G down to H. We study this problem systematically, both from the algebraic and the path integral points of view. We find that the usual BRST cohomology must be replaced by an equivariant version and that the ghost Lagrangian must always include quartic ghost terms, even at tree level. Both the Cartan and Weil models for equivariant cohomology play a role and find natural interpretations within the physics framework. Applications include the construction of D-brane models of emergent space, the 't Hooft's Abelian projection scenario in quantum chromodynamics and the formulation of the low energy effective theories of grand unified models.