Pure-spinor superstrings in d=2,4,6

TL;DR

This paper advances the understanding of pure-spinor superstring models in dimensions 2, 4, and 6 by solving constraints, analyzing algebraic structures, and exploring their relation to compactifications and hybrid models.

Contribution

It explicitly solves the pure-spinor constraints in these dimensions, analyzes the current algebra, and relates the models to superstring compactifications and hybrid superstrings.

Findings

Models have vanishing central charge.

Constructed covariant current algebra for Lorentz currents.

Established connections to superstring compactifications and hybrid models.

Abstract

We continue the study of the d=2,4,6 pure-spinor superstring models introduced in [1]. By explicitly solving the pure-spinor constraint we show that these theories have vanishing central charge and work out the (covariant) current algebra for the Lorentz currents. We argue that these super-Poincare covariant models may be thought of as compactifications of the superstring on CY_{4,3,2}, and take some steps toward making this precise by constructing a map to the RNS superstring variables. We also discuss the relation to the so called hybrid superstrings, which describe the same type of compactifications.