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arXiv · 1702.02861

Yang-Baxter $\sigma$-models, conformal twists, and noncommutative Yang-Mills theory

Thiago Araujo·Ilya Bakhmatov·Eoin Ó Colgáin·Jun-ichi Sakamoto·Mohammad M. Sheikh-Jabbari·Kentaroh Yoshida
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Abstract

The Yang-Baxter $\sigma$-model is a systematic way to generate integrable deformations of AdS$_5\times$S$^5$. We recast the deformations as seen by open strings, where the metric is undeformed AdS$_5\times$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 conditon on $r$-matrices for supergravity solutions translates into $\Theta$ being divergence-free. Integrability of the $\sigma$-model for unimodular $r$-matrices implies the existence and planar integrability of the dual NC gauge theory.

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Thiago Araujo, Ilya Bakhmatov, Eoin Ó Colgáin, Jun-ichi Sakamoto, Mohammad M. Sheikh-Jabbari, Kentaroh Yoshida. 2017-02-09. Yang-Baxter $\sigma$-models, conformal twists, and noncommutative Yang-Mills theory. https://doi.org/10.1103/physrevd.95.105006

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