Conformal twists, Yang–Baxter <i>σ</i>-models & holographic noncommutativity

DOI DOI Web Site Web Site Web Site View 1 Remaining Hide 6 Citations 98 References

Search this article

Description

Expanding upon earlier results [arXiv:1702.02861], we present a compendium of $��$-models associated with integrable deformations of AdS$_5$ generated by solutions to homogenous classical Yang-Baxter equation. Each example we study from four viewpoints: conformal (Drinfeld) twists, closed string gravity backgrounds, open string parameters and proposed dual noncommutative (NC) gauge theory. Irrespective of whether the deformed background is a solution to supergravity or generalized supergravity, we show that the open string metric associated with each gravity background is undeformed AdS$_5$ with constant open string coupling and the NC structure $��$ is directly related to the conformal twist. One novel feature is that $��$ exhibits "holographic noncommutativity": while it may exhibit non-trivial dependence on the holographic direction, its value everywhere in the bulk is uniquely determined by its value at the boundary, thus facilitating introduction of a dual NC gauge theory. We show that the divergence of the NC structure $��$ is directly related to the unimodularity of the twist. We discuss the implementation of an outer automorphism of the conformal algebra as a coordinate transformation in the AdS bulk and discuss its implications for Yang-Baxter $��$-models and self-T-duality based on fermionic T-duality. Finally, we comment on implications of our results for the integrability of associated open strings and planar integrability of dual NC gauge theories.

51 pages, 1 figure, LaTeX; v2 54 pages, presentation improved, references added; v3 appendix added to show that the relation between r-matrix and NC structure extends to modified CYBE; v4 published version

Journal

Citations (6)*help

See more

References(98)*help

See more

Related Projects

See more

Keywords

Report a problem

Back to top