Compactification of the Heterotic Pure Spinor Superstring I

TL;DR

This paper explores the compactification of the heterotic pure spinor superstring on Calabi-Yau backgrounds, deriving conditions for supersymmetry and matching the massless spectrum with theoretical expectations.

Contribution

It introduces a BRST operator for heterotic strings in Calabi-Yau backgrounds, linking nilpotence to geometric conditions and computing the massless spectrum.

Findings

BRST operator construction for heterotic strings in Calabi-Yau backgrounds

Nilpotence implies Kahler and Ricci-flatness conditions

Massless spectrum matches theoretical predictions

Abstract

In this paper we begin the study of compactifications of the pure spinor formalism for superstrings. As a first example of such a process we study the case of the heterotic string in a Calabi-Yau background. We explicitly construct a BRST operator imposing N=1 four-dimensional supersymmetry and show that nilpotence implies Kahler and Ricci-flatness conditions. The massless spectrum is computed using this BRST operator and it agrees with the expected result.