Quantum correction to generalized T-dualities

Abstract

Poisson-Lie duality is a generalization of abelian and non-abelian T-duality, and it can be viewed as a map between solutions of the low-energy effective equations of string theory, i.e. at the (super)gravity level. We show that this fact extends to the next order in ${\alpha }^{\prime }$ (two loops in $\sigma$-model perturbation theory) provided that the map is corrected. The ${\alpha }^{\prime }$-correction to the map is induced by the anomalous Lorentz transformations of the fields that are necessary to go from a doubled $O(D,D)$-covariant formulation to the usual (super)gravity description.

4 pages, plus 4 pages of supplemental material. 1 figure. Version 2: typos corrected, comments and references added. Title changed following a request by the journal's editor. Published version