Double supergeometry

A geometry of superspace corresponding to double field theory is developed, with type ii supergravity in d = 10 as the main example. the formalism is based on an orthosymplectic extension osp(d, d|2s) of the continuous t-duality group. covariance under generalised super-diffeomorphisms is manifest. ordinary superspace is obtained as a solution of the orthosymplectic section condition. a systematic study of curved superspace bianchi identities is performed, and a relation to a double pure spinor superfield cohomology is established. a ramond-ramond superfield is constructed as an infinite-dimensional orthosymplectic spinor. such objects in minimal orbits under the osp supergroup (“pure spinors”) define super-sections.