Compactification of the Heterotic Pure Spinor Superstring II

Abstract

We study compactifications of the heterotic pure spinor superstring to six and four dimensions focusing on two simple Calabi-Yau orbifolds. We show that the correct spectrum can be reproduced only if, in the twisted sector, there remain exactly 5 and 2 pure spinor components untwisted, respectively. This naturally defines a "small" Hilbert space of untwisted variables. We point out that the cohomology of the reduced differential on this small Hilbert space can be used to describe the states in the untwisted sector, provided certain auxiliary constraints are defined. In dimension six, the mismatch between the number of pure spinor components in the small Hilbert space and the number of components of a six-dimensional pure spinor is interpreted as providing the projective measure on the analytic subspace (in the projective description) of harmonic superspace.

Title changed. Added one reference

References in corpus (8)

• ICTP Lectures on Covariant Quantization of the Superstring
• The Character of Pure Spinors
• Lower-dimensional pure-spinor superstrings
• Compactification of the Heterotic Pure Spinor Superstring I
• Pure-spinor superstrings in d=2,4,6
• Non-Critical Pure Spinor Superstrings
• D=4 Pure Spinor Superstring and N=2 Strings
• On the Relation between Hybrid and Pure Spinor String Theory

Cited by in corpus (2)

• Six-dimensional Supergravity and Projective Superfields
• Superspaces for heterotic pure spinor string compactifications