Type II Double Field Theory in Superspace

TL;DR

This paper develops a superspace formulation of type II double field theory, introducing a supervielbein in OSp(10,10|64), and explores its geometric structure, symmetries, and Ramond-Ramond sector encoding.

Contribution

It presents the first superspace formulation of type II double field theory with an orthosymplectic supervielbein and analyzes its symmetry hierarchy and Ramond-Ramond sector.

Findings

Supervielbein in OSp(10,10|64) encodes supergeometry.

Infinite hierarchy of tangent space symmetries related to super-Maxwell∞ algebra.

Ramond-Ramond fields encoded as orthosymplectic spinors within supervielbein.

Abstract

We explore type II supersymmetric double field theory in superspace. The double supervielbein is an element of the orthosymplectic group OSp(10,10|64), which also governs the structure of generalized superdiffeomorphisms. Unlike bosonic double field theory, the local tangent space must be enhanced from the double Lorentz group in order to eliminate unphysical components of the supervielbein and to define covariant torsion and curvature tensors. This leads to an infinite hierarchy of local tangent space symmetries, which are connected to the super-Maxwell$_\infty$ algebra. A novel feature of type II is the Ramond-Ramond sector, which can be encoded as an orthosymplectic spinor (encoding the complex of super p-forms in conventional superspace). Its covariant field strength bispinor itself appears as a piece of the supervielbein. We provide a concise discussion of the superspace Bianchi identities through dimension two and show how to recover the component supersymmetry transformations of type II DFT. In addition, we show how the democratic formulation of type II superspace may be recovered by gauge-fixing.