Physics

T-duality

Pure mathematics

Mathematics

Mathematical physics

String theory

Abelian group

Duality (order theory)

Journal of High Energy Physics

A bstract Based on the construction of Poisson-Lie T -dual σ -models from a common parent action we study a candidate for the non-abelian respectively Poisson-Lie T -duality group. This group generalises the well-known abelian T -duality group O( d, d ) and we explore some of its subgroups, namely factorised dualities, B - and β -shifts. The corresponding duality transformed σ -models are constructed and interpreted as generalised (non-geometric) flux backgrounds. We also comment on generalisations of results and techniques known from abelian T -duality. This includes the Lie algebra cohomology interpretation of the corresponding non-geometric flux backgrounds, remarks on a double field theory based on non-abelian T -duality and an application to the investigation of Yang-Baxter deformations. This will show that homogeneously Yang-Baxter deformed σ -models are exactly the non-abelian T -duality β -shifts when applied to principal chiral models.

Generalised fluxes, Yang-Baxter deformations and the O(d,d) structure of non-abelian T -duality