Path-integral derivation of quantum duality in nonlinear sigma-models

Abstract

We show that a previously derived shift in the dilaton field, which necessarily augments the classical effects of duality transformation on the geometry of a nonlinear sigma-model if conformal invariance is to be preserved at the one-loop level, can be extended without change to the case of sigma-models with Wess-Zumino-Witten term (torsion) before and after duality. We also construct a path-integral implementation of the duality transformation, and discover the origin of the dilaton shift in a functional determinant resulting from the elimination of the first-order field. The path-integral formulation in principle allows a derivation of “quantum” duality transformations which preserve conformal invariance to all orders in α', the string tension parameter.