Abstract
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 \( \mathcal{C} \)3 ⨁ \( \mathcal{A} \)1,1 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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This work has been supported by the research vice chancellor of Azarbaijan Shahid Madani University under research fund No. 1402/537.
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The paper is dedicated to the fond memory of professor Farhad Darabi who passed away on 13 Sept 2022.
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Eghbali, A., Hosseinpour-Sadid, M. & Rezaei-Aghdam, A. T-duality/plurality of BTZ black hole metric coupled to two fermionic fields. J. High Energ. Phys. 2024, 40 (2024). https://doi.org/10.1007/JHEP03(2024)040
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DOI: https://doi.org/10.1007/JHEP03(2024)040