Exploring the geometry of supersymmetric double field theory

TL;DR

This paper investigates the geometric structure of N=1 supersymmetric double field theory in superspace, revealing an extended tangent space group and deriving supersymmetry transformations and equations of motion.

Contribution

It introduces an expanded tangent space group including higher dimension generators and derives the superspace geometry and equations of motion for supersymmetric double field theory.

Findings

Extended tangent space group with higher generators.

Explicit superspace Bianchi identities solved up to dimension two.

Component supersymmetry transformations and equations of motion derived.

Abstract

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) x 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$_\infty$ 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.