Superfield approach to BRST cohomology

TL;DR

This paper explores the cohomological structure of a 2D free Abelian gauge theory using superfield formalism, revealing how BRST charges generate translations on a supermanifold and relate to de Rham cohomology operators.

Contribution

It demonstrates the geometric interpretation of BRST and co-BRST charges as translation generators on a supermanifold, connecting gauge symmetry with differential geometry.

Findings

BRST charges generate translations along Grassmannian directions.

Bosonic symmetry corresponds to combined Grassmannian translations.

Charges are analogous to de Rham cohomology operators.

Abstract

In the framework of superfield formalism, we discuss some aspects of the cohomological features of a two (1+1)-dimensional free Abelian gauge theory described by a Becchi-Rouet-Stora-Tyutin (BRST) invariant Lagrangian density. We demonstrate that the conserved and nilpotent (anti-)BRST- and (anti-)co-BRST charges are the generators of translations along the Grassmannian directions of the four (2+2)-dimensional supermanifold. A bosonic symmetry is shown to be generated by a Noether conserved charge that generates a translation along a bosonic direction of the supermanifold which turns out to be equivalent to a couple of successive translations along the two different and independent Grassmannian directions of the same supermanifold. Algebraically, these charges are found to be analogous to the de Rham cohomology operators of differential geometry.