Abstract
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.
Highlights
A geometry of superspace corresponding to double field theory is developed, with type II supergravity in D = 10 as the main example
Unlike previous work on double supergeometry [1,2,3], our formalism does not use any input from string theory in terms of world-sheet algebras
If supersymmetry is to be made manifest in terms of superfields, it seems necessary that superspace, even in the flat case, has an interpretation as supergeometry
Summary
The geometric formulation of double field theory [18] (see refs. [7, 13, 16]) is well known. The second form of R is maybe not very useful compared to the first one It conveys one very important piece of information, which is not manifest from its expression in the affine connection, namely, that it only gets contributions from terms where at least one of the two pairs takes values in so(d) ⊕ so(d). If supersymmetry is to be made manifest in terms of superfields, it seems necessary that superspace, even in the flat case, has an interpretation as supergeometry It does not seem consistent with super-diffeomorphisms to constrain a bosonic corner of a super-vielbein, or even to consider a bosonic part of a vector to transform under a restricted subgroup. We will come back to this issue in the conclusions of section 6, as it turns out that the behaviour of the RamondRamond fields in double supergeometry points strongly towards infinite-dimensional supergroups in the exceptional cases
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