$(1, 0)$-Covariant supergraphs

Covariant methods are developed for calculation of the superconformal anomaly in terms of $(1,0)$-superfields for the heterotic string on a nontrivial background. The approach is based on the generalized proper time method in a $(1,0)$-curved superspace using a supersymmetric and reparametrization-invariant regularization with respect to the proper time. The structure of the superfield propagators in the ultraviolet limit is investigated.