Holomorphicity and Non-holomorphicity in N = 2 Supersymmetric Field Theories

Abstract

A quantum field theory usually comes with parameters such as coupling constants and configuration of background fields. In such a case, it is often useful to consider a family of quantum field theories with various values of the parameters and to examine how various physical observables depend on the parameters. In particular, when the theory has N = 2 supersymmetry, a large class of amplitudes become holomorphic or quasi-holomorphic with respect to these parameters, and in some cases the holomorphic property combined with some global consideration determines these amplitudes uniquely. Here I would like to discuss how such an idea can be applied to the case of the N = 2 supersymmetric sigma-model in two dimensions when the target space is a Calabi-Yau manifold.