Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local $\beta$-deformations and Yang-Baxter sigma model   Homogeneous Yang-Baxter (YB) deformation of AdS$_5\times$S$^5$ superstring is
revisited. We calculate the YB sigma model action up to quadratic order in
fermions and show that homogeneous YB deformations are equivalent to
$\beta$-deformations of the AdS$_5\times$S$^5$ background when the classical
$r$-matrices consist of bosonic generators. In order to make our discussion
clearer, we discuss YB deformations in terms of the double-vielbein formalism
of double field theory. We further provide an O(10,10)-invariant string action
that reproduces the Green-Schwarz type II superstring action up to quadratic
order in fermions. When an AdS background contains a non-vanishing $H$-flux, it
is not straightforward to perform homogeneous YB deformations. In order to get
any hint for such YB deformations, we study $\beta$-deformations of $H$-fluxed
AdS backgrounds and obtain various solutions of (generalized) type II
supergravity.

16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg