Chiral fermions on 2D curved space–times

Abstract

The theory of free Majorana–Weyl spinors is the prototype of conformal field theory in two dimensions in which the gravitational anomaly and the Weyl anomaly obstruct extending the flat space–time results to curved backgrounds. In this paper, we investigate a quantization scheme in which the short distance singularity in the two-point function of chiral fermions on a two-dimensional curved space–time is given by the Green’s function corresponding to the classical field equation. We compute the singular term in the Green’s function explicitly and observe that the short distance limit is not well-defined in general. We identify constraints on the geometry which are necessary to resolve this problem. On such special backgrounds, the theory has locally [Formula: see text] conformal symmetry.