Extended Riemannian Geometry I: Local Double Field Theory

TL;DR

This paper develops an extended Riemannian geometry framework using graded manifolds to better understand double field theory and related duality-invariant field theories, unifying various geometric and gauge structures.

Contribution

It introduces an extended Riemannian geometry based on graded manifolds, providing new insights into symmetries, constraints, and covariant formulations in double field theory.

Findings

Recovers general relativity with gauge potentials as special cases

Provides a covariant form of the strong section condition

Facilitates global, coordinate-invariant descriptions of duality-invariant theories

Abstract

We present an extended version of Riemannian geometry suitable for the description of current formulations of double field theory (DFT). This framework is based on graded manifolds and it yields extended notions of symmetries, dynamical data and constraints. In special cases, we recover general relativity with and without 1-, 2- and 3-form gauge potentials as well as DFT. We believe that our extended Riemannian geometry helps to clarify the role of various constructions in DFT. For example, it leads to a covariant form of the strong section condition. Furthermore, it should provide a useful step towards global and coordinate invariant descriptions of T- and U-duality invariant field theories.