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.Comment: 85 pages; v2: references added, additional comments in introduction
and conclusio