Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Yang-Baxter $\sigma$-models, conformal twists, and noncommutative
  Yang-Mills theory   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.

25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph