Supersymmetric Double Field Theory: Stringy Reformulation of Supergravity

We construct a supersymmetric extension of double field theory that realizes the ten-dimensional Majorana-Weyl local supersymmetry. In terms of a stringy differential geometry we proposed earlier, our action consists of five simple terms -- two bosonic plus three fermionic -- and manifests not only diffeomorphism and one-form gauge symmetry of B-field, but also O(10,10) T-duality as well as a direct product of two local Lorentz symmetries, SO(1,9) \times SO(9,1). A gauge fixing that identifies the double local Lorentz groups reduces our action to the minimal supergravity in ten dimensions.