BRST and Anti BRST structure of a topological current algebra

TL;DR

This paper explores the combined BRST and anti-BRST structures of a topological current algebra, revealing an N=4 Superconformal algebra with an infinite-dimensional structure and vanishing central charge in most operator product expansions.

Contribution

It extends previous work by analyzing the full BRST and anti-BRST structure, resulting in an infinite-dimensional N=4 Superconformal algebra with simplified central charge behavior.

Findings

Derivation of an N=4 Superconformal algebra from topological current algebra.

Most operator product expansions have zero central charge.

The algebra becomes infinite-dimensional due to proliferation of operators.

Abstract

The BRST structure of a current satisfying a non abelian affine algebra in two dimensions was studied by Isidro and Ramallo and an N=2 Superconformal Algebra was obtained. In this paper, we study the total BRST and anti BRST structure of the topological algebra. We end up with an N=4 Superconformal algebra in which the central charge drops out of most of the OPE's. The price one has to pay is that the no. of operators proliferates tremendously and the algebra becomes infinite dimensional.