BRST Operator for Superconformal Algebras with Quadratic Nonlinearity

TL;DR

This paper constructs quantum BRST operators for a broad class of superconformal algebras with quadratic nonlinearity, revealing conditions on the level parameter for nilpotency.

Contribution

It introduces a method to construct quantum BRST operators for quadratic superconformal algebras and determines the level conditions for nilpotency.

Findings

Derived nilpotency conditions for various superconformal algebras

Extended BRST construction to quadratic nonlinear algebras

Analyzed algebras based on simple Lie and superalgebras

Abstract

We construct the quantum BRST operators for a large class of superconformal and quasi--superconformal algebras with quadratic nonlinearity. The only free parameter in these algebras is the level of the (super) Kac-Moody sector. The nilpotency of the quantum BRST operator imposes a condition on the level. We find this condition for (quasi) superconformal algebras with a Kac-Moody sector based on a simple Lie algebra and for the $Z_2\times Z_2$--graded superconformal algebras with a Kac-Mody sector based on the superalgebra $osp(N\vert 2M)$ or $s\ell(N+2\vert N)$.