Compactification of the Heterotic Pure Spinor Superstring I

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.