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Conformal twists, Yang–Baxter <i>σ</i>-models & holographic noncommutativity
Araujo, Thiago,Bakhmatov, Ilya,Colgá,in, Eoin Ó,Sakamoto, Jun-ichi,Sheikh-Jabbari, Mohammad M,Yoshida, Kentaroh IOP 2018 JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL Vol.51 No.23
<P>Expanding upon earlier results (Araujo <I>et al</I> 2017 <I>Phys. Rev</I>. D <B>95</B> 105006), we present a compendium of <I>σ</I>-models associated with integrable deformations of AdS<SUB>5</SUB> 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<SUB>5</SUB> with constant open string coupling and the NC structure 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 a dual NC gauge theory. We show that the divergence of the NC structure Θ 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 <I>σ</I>-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.</P>
Yang-Baxter σ -models, conformal twists, and noncommutative Yang-Mills theory
Araujo, T.,Bakhmatov, I.,Colgá,in, E. Ó,.,Sakamoto, J.,Sheikh-Jabbari, M. M.,Yoshida, K. American Physical Society 2017 Physical Review D Vol.95 No.10
<P>The Yang-Baxter s-model is a systematic way to generate integrable deformations of AdS(5) x S-5. We recast the deformations as seen by open strings, where the metric is undeformed AdS(5) x S-5 with constant string coupling, and all information about the deformation is encoded in the noncommutative (NC) parameter Theta. We identify the deformations of AdS(5) as twists of the conformal algebra, thus explaining the noncommutativity. We show that the unimodularity condition on gamma-matrices for supergravity solutions translates into Theta being divergence-free. Integrability of the s-model for unimodular sigma-matrices implies the existence and planar integrability of the dual NC gauge theory.</P>