Superspaces for heterotic pure spinor string compactifications

We study supersymmetry conditions for the heterotic pure superstring preserving N=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N=1$$\end{document} supersymmetry in four dimensions directly from the curved superspace defined by the Berkovits–Howe constraints.