$N=1$ Superstring in $2+2$ Dimensions

TL;DR

This paper constructs a novel $(2,2)$ dimensional superstring theory with manifest $N=1$ supersymmetry, exploring its algebraic structure and physical states through two different methods, including BRST cohomology and covariant approaches.

Contribution

It introduces a new superstring model in 2+2 dimensions with a twisted superconformal algebra and analyzes its physical states using innovative reducible and covariant methods.

Findings

Identified a critical subset of irreducible constraints.

Constructed the BRST operator and studied cohomology.

Developed a covariant formulation with ghosts for ghosts.

Abstract

In this paper we construct a $(2,2)$ dimensional string theory with manifest $N=1$ spacetime supersymmetry. We use Berkovits' approach of augmenting the spacetime supercoordinates by the conjugate momenta for the fermionic variables. The worldsheet symmetry algebra is a twisted and truncated ``small'' $N=4$ superconformal algebra. The realisation of the symmetry algebra is reducible with an infinite order of reducibility. We study the physical states of the theory by two different methods. In one of them, we identify a subset of irreducible constraints, which is by itself critical. We construct the BRST operator for the irreducible constraints, and study the cohomology and interactions. This method breaks the $SO(2,2)$ spacetime symmetry of the original reducible theory. In another approach, we study the theory in a fully covariant manner, which involves the introduction of infinitely many ghosts for ghosts.