Exploring Double Field Theory

TL;DR

This work develops a flux-centered formulation of Double Field Theory in which geometric and non-geometric fluxes are dynamical and field-dependent. By deriving generalized gauge constraints and constructing covariant generalized connections, curvatures, and a Ricci scalar without imposing the strong constraint, it reveals the systematic appearance of strong-constraint–violating terms that reproduce duality orbits of non-geometric fluxes upon Scherk–Schwarz reductions. The framework is extended to Type II and heterotic theories with RR and vector sectors, and Bianchi identities are organized into a unified, duality-covariant scheme that accommodates sources such as NS5-branes, KK5-monopoles, and exotic branes like $5^2_2$. This approach offers a pathway to truly doubled backgrounds and non-geometric backgrounds, enabling a covariant treatment of brane sources and their flux-induced gaugings, with several open questions about the string-theoretic validity of relaxed constraints and full U-duality completion.

Abstract

We present a flux formulation of Double Field Theory, in which geometric and non-geometric fluxes are dynamical and field-dependent. Gauge consistency imposes a set of quadratic constraints on the dynamical fluxes, which can be solved by truly double configurations. The constraints are related to generalized Bianchi Identities for (non-)geometric fluxes in the double space, sourced by (exotic) branes. Following previous constructions, we then obtain generalized connections, torsion and curvatures compatible with the consistency conditions. The strong constraint-violating terms needed to make contact with gauged supergravities containing duality orbits of non-geometric fluxes, systematically arise in this formulation.