A complex geometric perspective on a,c anomalies

In four-dimensional conformal field theory, the numbers a and c are defined as coefficients of particular terms in the operator product expansion (OPE) of the energy-momentum tensor. With supersymmetry there are relations between these coefficients and mixed R-symmetry and gravitational anomalies. In this paper we prove a relationship between these coefficients and anomalies to holomorphic reparametrization symmetry at the level of the holomorphic twist.