Abstract

It is well-known that the beta functions on a string worldsheet correspond to the target space equations of motion, e.g. the Einstein equations. We show that the BPS equations, i.e. the conditions of vanishing supersymmetry variations of the space-time fermions, can be directly derived from the worldsheet. To this end we consider a heterotic worldsheet model in the RNS -formulation with (2,0) supersymmetry, which describes a complex torsion target space that supports a holomorphic vector bundle. After a detailed account of its quantization and renormalization, we establish that super Weyl anomaly cancellation implies the heterotic BPS conditions: At the one loop level the geometry is required to be conformally balanced and the gauge background has to satisfy the Hermitean Yang-Mills equations.