Exploring the geometry of supersymmetric double field theory

The geometry of N=1 supersymmetric double field theory is revisited in superspace. In order to maintain the constraints on torsion tensor, local tangent space group O(D) x must be expanded include a tower higher dimension generators. These generator irreducible hook representation Lorentz group, which gauges shift symmetry (or ambiguity) spin connection. This gauging possible even purely bosonic theory, where it leads curvature whose only non-vanishing pieces are physical ones: generalized Einstein tensor and scalar curvature. A relation super-Maxwell$_\infty$ algebra proposed. superspace Bianchi identities solved up through two, component supersymmetry transformations equations motion explicitly (re)derived.