Non-Critical Pure Spinor Superstrings

TL;DR

This paper constructs non-critical pure spinor superstrings in lower dimensions, maps them to RNS variables, analyzes their structure and anomalies, and extends the framework to curved backgrounds like AdS_4 with flux.

Contribution

It introduces explicit constructions of non-critical pure spinor superstrings in 2, 4, and 6 dimensions, including the mapping to RNS variables and analysis of their properties.

Findings

Explicit map between RNS and pure spinor variables in non-critical backgrounds

Analysis of pure spinor space and quantum anomalies in lower dimensions

Construction of non-critical pure spinor superstring on AdS_4 with flux

Abstract

We construct non-critical pure spinor superstrings in two, four and six dimensions. We find explicitly the map between the RNS variables and the pure spinor ones in the linear dilaton background. The RNS variables map onto a patch of the pure spinor space and the holomorphic top form on the pure spinor space is an essential ingredient of the mapping. A basic feature of the map is the requirement of doubling the superspace, which we analyze in detail. We study the structure of the non-critical pure spinor space, which is different from the ten-dimensional one, and its quantum anomalies. We compute the pure spinor lowest lying BRST cohomology and find an agreement with the RNS spectra. The analysis is generalized to curved backgrounds and we construct as an example the non-critical pure spinor type IIA superstring on AdS_4 with RR 4-form flux.