Generalized Dualities and Supergroups

TL;DR

This paper develops a unified framework using double superspace to encode supergravity fields and dualities, extending known duality groups and applying it to integrable deformations of superstrings.

Contribution

It introduces a generalized supervielbein in double superspace that encodes supergravity fields and extends duality transformations to supergroups, including applications to deformations of the $AdS_5 imes S^5$ superstring.

Findings

Unified supergeometry framework for supergravity fields.

Extended duality group to orthosymplectic transformations.

Explicit construction of supergeometries for integrable deformations.

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 $\lambda$ and $\eta$ deformations of the $AdS_5 \times S^5$ superstring. The deformation parameters $\lambda$ and $\eta$ 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.