Anomalies as curvature in complex geometry

Abstract

We study two-dimensional bosonic and fermionic field theories in the language of infinite-dimensional complex geometry. We show that all local (“perturbative”) anomalies canbe interpreted as curvature of a Fock bundle over the space of complex structures. We discuss the example of the gauge anomaly of a chiral fermion in detail. A method to compute the curvature of a homogeneous hermitian holomorphic vector bundle is developed in the appendix.