Yang-Baxter σ -models, conformal twists, and noncommutative Yang-Mills theory

The Yang-Baxter σ-model is a systematic way to generate integrable deformations of AdS5×S5. We recast the deformations as seen by open strings, where the metric is undeformed AdS5×S5 with constant string coupling, and all information about the deformation is encoded in the noncommutative (NC) parameter Θ. We identify the deformations of AdS5 as twists of the conformal algebra, thus explaining the noncommutativity. We show that the unimodularity condition on r-matrices for supergravity solutions translates into Θ being divergence-free. Integrability of the σ-model for unimodular r-matrices implies the existence and planar integrability of the dual NC gauge theory.