  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.
