BRST Charge for the Orthogonal Series of Bershadsky-Knizhnik Quasi-Superconformal Algebras

TL;DR

This paper constructs the quantum BRST charges for specific superconformal algebras with N=4 supersymmetry, revealing a unique solution and proposing a new string theory with non-linear supersymmetry and negative critical dimension.

Contribution

It provides the first explicit construction of BRST charges for the Bershadsky-Knizhnik orthogonal quasi-superconformal algebras and identifies conditions for their nilpotency.

Findings

Unique BRST charge solution at N=4, k=-2

Existence of a new string theory with N=4 supersymmetry

Proposal of a string theory with negative critical dimension

Abstract

The quantum BRST charges for the Bershadsky-Knizhnik orthogonal quasi-superconformal algebras are constructed. These two-dimensional superalgebras have the $N$-extended non-linearly realised supersymmetry and the $SO(N)$ internal symmetry. The BRST charge nilpotency conditions are shown to have a unique solution at $N>2$, namely, $N=4$ and $k=-2$, where $k$ is central extension parameter of the Ka\v{c}-Moody subalgebra. We argue about the existence of a new string theory with the non-linearly realised $N=4$ world-sheet supersymmetry and negative `critical dimension'.