Generalised fluxes, Yang-Baxter deformations and the O\((d,d)\) structure of non-abelian \(T\)-duality. (English) Zbl 1391.83115
Summary: Based on the construction of Poisson-Lie \(T\)-dual \(\sigma\)-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 \(\beta\)-shifts. The corresponding duality transformed \(\sigma\)-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 \(\sigma\)-models are exactly the non-abelian \(T\)-duality \(\beta\)-shifts when applied to principal chiral models.
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 \(\sigma\)-models are exactly the non-abelian \(T\)-duality \(\beta\)-shifts when applied to principal chiral models.
MSC:
| 83E30 | String and superstring theories in gravitational theory |
| 81R12 | Groups and algebras in quantum theory and relations with integrable systems |
| 83C65 | Methods of noncommutative geometry in general relativity |
| 16T25 | Yang-Baxter equations |
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