  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 the RNS-formulation of the heterotic string 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 the cancellation of the Weyl anomaly
combined with (2,0) finiteness 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.
