Generalized Dualities and Supergroups
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866916403496353792 |
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| author | Butter, Daniel Hassler, Falk Pope, Christopher N. Zhang, Haoyu |
| author_facet | Butter, Daniel Hassler, Falk Pope, Christopher N. Zhang, Haoyu |
| contents | 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 $AdS_5 \times S^5$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_05665 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Generalized Dualities and Supergroups Butter, Daniel Hassler, Falk Pope, Christopher N. Zhang, Haoyu High Energy Physics - Theory 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 $AdS_5 \times S^5$ 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. |
| title | Generalized Dualities and Supergroups |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2307.05665 |