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Paper   IPM / Physic / 14779
School of Physics
  Title:   Conformal Twists, Yang-Baxter σ-models and Holographic Noncommutativity
  Author(s): 
1.  T. Araujo
2.  I. Bakhmatov
3.  E. \'O Colg\'ain
4.  J. Sakamoto
5.  M.M. Sheikh-Jabbari
6.  K. Yoshida
  Status:   Published
  Journal: J. Phys. A: Math. Theor.
  Vol.:  51
  Year:  2018
  Pages:   235401
  Supported by:  IPM
  Abstract:
Expanding upon earlier results [arXiv:1702.02861], we present a compendium of Yang-Baxter σ-models associated with integrable deformations of AdS5. Each example we study from four viewpoints: conformal Drinfeld twists, closed string gravity backgrounds, open string parameters and 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 AdS5 with constant open string coupling and the NC parameter Θ is directly related to the conformal twist. One novel feature is that Θ 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 the dual NC gauge theory. We show that the divergence of the NC parameter Θ is directly related to the unimodularity of the twist. We discuss the implementation of an outer automorphism of AdS as a coordinate transformation in the bulk and discuss its implications for Yang-Baxter σ-models and self-T-duality based on fermionic T-duality. Finally, we discuss implications of our results for the integrability of associated open strings and planar integrability of dual NC gauge theories.

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