BRST structure of non-linear superalgebras

TL;DR

This paper investigates the structure of the BRST charge in quadratic nonlinear superalgebras, deriving explicit forms and constraints, thus advancing understanding of their algebraic properties in gauge theories.

Contribution

It provides explicit formulas for the BRST charge up to cubic order and identifies constraints on structure constants for quadratic nonlinear superalgebras.

Findings

Explicit form of BRST charge up to cubic order.

Existence of constraints on structure constants.

Illustrative examples of superalgebras.

Abstract

In this paper we analyse the structure of the BRST charge of nonlinear superalgebras. We consider quadratic non-linear superalgebras where a commutator (in terms of (super) Poisson brackets) of the generators is a quadratic polynomial of the generators. We find the explicit form of the BRST charge up to cubic order in Faddeev-Popov ghost fields for arbitrary quadratic nonlinear superalgebras. We point out the existence of constraints on structure constants of the superalgebra when the nilpotent BRST charge is quadratic in Faddeev-Popov ghost fields. The general results are illustrated by simple examples of superalgebras.