Double supergeometry

TL;DR

This paper develops a superspace geometry framework aligned with double field theory, extending T-duality symmetries to supersymmetric contexts, and introduces novel superfield constructions and cohomological structures.

Contribution

It introduces a formalism based on orthosymplectic extension OSp(d,d|2s) for superspace geometry in double field theory, including new superfield and cohomology concepts.

Findings

Covariance under super-diffeomorphisms is explicit.

Ordinary superspace emerges from the orthosymplectic section condition.

Constructed a Ramond-Ramond superfield as an infinite-dimensional orthosymplectic spinor.

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.