Abstract

Berry phase is a well-known feature of quantum mechanics. In this talk I will discuss several new results about Berry phase in quantum field theory. We will see that even simple quantum field theories can exhibit non-trivial Berry phases and will discuss an explicit example in axion electrodynamics. We will also discuss a general relation between the Berry connection in conformal field theories and the connections on conformal manifolds considered previously by several authors in conformal perturbation theory. The implementation of this relation in 2d N=(2,2) and 4d N=2 superconformal field theories leads to a useful re-derivation of the tt* equations. The latter have important implications on the non-perturbative structure of certain correlation functions in supersymmetric theories, which I will briefly review.