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Abstract
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We ask the question of classical super (non-)Abelian T-duality for BTZ black
hole metric coupling to two fermionic fields. Our approach is based on super Poisson-Lie
(PL) T-duality in the presence of spectator fields. In order to study the Abelian T-duality
of the metric we dualize over the Abelian Lie supergroups of the types (1|2) and (2|2), in
such a way that it is shown that both original and dual backgrounds of the models are
conformally invariant up to one-loop order in the presence of field strength. Then, we study
the non-Abelian T-duality of the BTZ vacuum metric coupling to two fermionic fields. The
dualizing is performed on some non-Abelian Lie supergroups of the type (2|2), in such a
way that we are dealing with semi-Abelian superdoubles which are non-isomorphic as Lie
superalgebras in each of the models. In the non-Abelian T-duality case, it is interesting to
mention that the models can be conformally invariant up to one-loop order in both cases of
the absence and presence of field strength. In addition, starting from the decomposition of
semi-Abelian Drinfeld superdoubles generated by some of the C 3 ⊕ A1,1 Lie superbialgebras
we study the super PL T-plurality of the BTZ vacuum metric coupled to two fermionic
fields. However, our findings are interesting in themselves, but at a constructive level, can
prompt many new insights into supergravity and manifestly have interesting mathematical
relationships with double field theory.
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