Generalized dualities and supergroups

Abstract

jats:titleAjats:scbstract</jats:sc> </jats:title>jats:pUsing a recently developed formulation of double field theory in superspace, the graviton, jats:italicB</jats:italic>-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(jats:italicD</jats:italic>, jats:italicD</jats:italic>) 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.</jats:p>jats:pWe then extend this approach to include Poisson-Lie T-duality and its generalizations, including the generalized coset construction recently discussed in [<jats:ext-link xmlns:xlink="http://www.w3.org/1999/xlink" ext-link-type="uri" xlink:href="https://arxiv.org/abs/1912.11036]">arXiv:1912.11036</jats:ext-link>]. As an application, we construct the supergeometries associated with the integrable jats:italicλ</jats:italic> and jats:italicη</jats:italic> deformations of the AdSjats:sub5</jats:sub> × Sjats:sup5</jats:sup> superstring. The deformation parameters jats:italicλ</jats:italic> and jats:italicη</jats:italic> 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.</jats:p>