A Superstring Theory in 2+2 Dimensions

TL;DR

This paper develops a novel superstring theory in 2+2 dimensions with manifest supersymmetry, revealing an infinite spectrum of massless states including self-dual and anti-self-dual Yang-Mills multiplets and their higher-spin generalizations.

Contribution

It constructs a new superstring model in 2+2 dimensions with a specific worldsheet symmetry algebra and detailed spectrum analysis, extending previous theories to include higher-spin multiplets.

Findings

Infinite massless spectrum including self-dual and anti-self-dual Yang-Mills multiplets

Worldsheet symmetry algebra is a twisted small N=4 superconformal algebra

Higher-spin multiplets are natural extensions of basic multiplets

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 physical spectrum of the open string contains an infinite number of massless states, including a supermultiplet of a self-dual Yang-Mills field and a right-handed spinor and a supermultiplet of an anti-self-dual Yang-Mills field and a left-handed spinor. The higher-spin multiplets are natural generalisations of these self-dual and anti-self-dual multiplets.