1998/03/31 by Konstadinos Sfetsos
Mathematics · Physics and Astronomy · #Abelian group #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Duality (order theory) #Equivalence (formal languages) #Fixed point #Lie group #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Poisson distribution #Pure mathematics #Renormalization group #String theory #T-duality #hep-th
paper · pdf · doi:10.1016/s0370-2693(98)00666-2
published as Phys.Lett. B432 (1998) 365-375 · 13 pages, latex; v2: references and a note are added. Version to appear in Phys. Lett. B
arxiv created 1998/05/26 · openalex publication_date 1998/07/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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 S3 and S2. 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.