Abstract
The geometry of mathcal{N} = 1 supersymmetric double field theory is revisited in superspace. In order to maintain the constraints on the torsion tensor, the local tangent space group of O(D) × O(D) must be expanded to include a tower of higher dimension generators. These include a generator in the irreducible hook representation of the Lorentz group, which gauges the shift symmetry (or ambiguity) of the spin connection. This gauging is possible even in the purely bosonic theory, where it leads to a Lorentz curvature whose only non-vanishing pieces are the physical ones: the generalized Einstein tensor and the generalized scalar curvature. A relation to the super-Maxwell∞ algebra is proposed. The superspace Bianchi identities are solved up through dimension two, and the component supersymmetry transformations and equations of motion are explicitly (re)derived.
Highlights
Double field theory (DFT) is a formulation of the massless sector of string theory that makes T -duality manifest [1,2,3,4,5,6]
The geometry of N = 1 supersymmetric double field theory is revisited in superspace
In order to maintain the constraints on the torsion tensor, the local tangent space group of O(D) × O(D) must be expanded to include a tower of higher dimension generators
Summary
Double field theory (DFT) is a formulation of the massless sector of string theory that makes T -duality manifest [1,2,3,4,5,6]. What we discover in superspace is this new local symmetry is required by closure of the extended tangent space algebra In other words, it transforms a “bug” of DFT into a “feature.”. This is largely for review and to fix notation, but we elaborate on the shift symmetry of the spin connection and how the introduction of the higher connection h permits one to build a Lorentz curvature tensor with only physical components. Particular attention is paid to how the tangent space group is used to eliminate unphysical components of the vielbein
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