Abstract
Using a recently developed formulation of double field theory in superspace, the graviton, B-field, gravitini, dilatini, and Ramond-Ramond bispinor are encoded in a single generalized supervielbein. Duality transformations are encoded as orthosymplectic transformations, extending the bosonic O(D, D) duality group, and these act on all constituents of the supervielbein in an easily computable way. We first review conventional non-abelian T-duality in the Green-Schwarz superstring and describe the dual geometries in the language of double superspace. Since dualities are related to super-Killing vectors, this includes as special cases both abelian and non-abelian fermionic T-duality.
We then extend this approach to include Poisson-Lie T-duality and its generalizations, including the generalized coset construction recently discussed in [arXiv:1912.11036]. As an application, we construct the supergeometries associated with the integrable λ and η deformations of the AdS5 × S5 superstring. The deformation parameters λ and η are identified with the possible one-parameter embeddings of the supergravity frame within the doubled supergeometry. In this framework, the Ramond-Ramond bispinors are directly computable purely from the algebraic data of the supergroup.
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Acknowledgments
We would like to thank Riccardo Borsato, Sybille Driesen, Gabriel Larios, Grégoire Josse, Edvard Musaev, Yuho Sakatani, and Linus Wulff for helpful discussions, and Evgeny Ivanov, Martin Wolf, Pietro Grassi, Peter West, and Ali Eghbali for helpful comments. FH wants to thank the organizers of the workshop “Supergravity, Strings and Branes” at Bogazici University, Turkey for giving him the opportunity to present this work. The work of FH is supported by the SONATA BIS grant 2021/42/E/ST2/00304 from the National Science Centre (NCN), Poland. CNP is supported in part by DOE grant DE-FG02-13ER42020.
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Butter, D., Hassler, F., Pope, C.N. et al. Generalized dualities and supergroups. J. High Energ. Phys. 2023, 52 (2023). https://doi.org/10.1007/JHEP12(2023)052
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DOI: https://doi.org/10.1007/JHEP12(2023)052