Poisson-Lie T-Duality beyond the classical level and the renormalization group

Abstract

In order to study quantum aspects of $\s$-models related by Poisson--Lie T-duality, we construct three- and two-dimensional models that correspond, in one of the dual faces, to deformations of $S^3$ and $S^2$. Their classical canonical equivalence is demonstrated by means of a generating functional, which we explicitly compute. We examine how they behave under the renormalization group and show that dually related models have the same 1-loop beta functions for the coupling and deformation parameters. We find non-trivial fixed points in the ultraviolet, where the theories do not become asymptotically free. This suggests that the limit of Poisson--Lie T-duality to the usual Abelian and non-Abelian T-dualities does not exist quantum mechanically, although it does so classically.

13 pages, latex; v2: references and a note are added. Version to appear in Phys. Lett. B

References in corpus (2)

• Duality and Dilaton
• Canonical equivalence of non-isometric sigma models and Poisson-Lie T-duality

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