Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-Abelian T-duality of $AdS_{d\le3}$ families by Poisson-Lie T-duality   We proceed to investigate the non-Abelian T-duality of $AdS_{2}$,
$AdS_{2}\times S^1$ and $AdS_{3}$ physical backgrounds, as well as the metric
of the analytic continuation of $AdS_{2}$ from the point of view of Poisson-Lie
(PL) T-duality. To this end, we reconstruct these metrics of the $AdS$ families
as backgrounds of non-linear $\sigma$-models on two- and three-dimensional Lie
groups. By considering the Killing vectors of these metrics and by taking into
account the fact that the subgroups of isometry Lie group of the metrics can be
taken as one of the subgroups of the Drinfeld double (with Abelian duals) we
look up the PL T-duality. To construct the dualizable metrics by the PL
T-duality we find all subalgebras of Killing vectors that generate subgroup of
isometries which acts freely and transitively on the manifolds defined by
aforementioned $AdS$ families. We then obtain the dual backgrounds for these
families of $AdS$ in such a way that we apply the usual rules of PL T-duality
without further corrections. Meanwhile, we have shown that all original
backgrounds ($AdS$ families) are conformally invariant up to two-loop order,
while this is not the case for dual solutions. Finally, by using the T-duality
rules proposed by Kaloper and Meissner (KM) we calculate the Abelian T-duals of
BTZ black hole up to two-loop by dualizing on the coordinates $ \varphi$ and $
t $. When the dualizing is implemented by the shift of direction $\varphi$, we
show that the horizons and singularity of the dual spacetime are the same as in
charged black string derived by Horne and Horowitz without
$\alpha'$-corrections, whereas in dualizing on the coordinate $t$ we find a new
three-dimensional black string whose structure and asymptotic nature are
clearly determined. For this case, we show that the T-duality transformation
changes the asymptotic behavior from $AdS_3$ to flat.

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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio