Double Field Theory: A Pedagogical Review

TL;DR

This paper provides a comprehensive pedagogical overview of Double Field Theory, explaining its foundations, construction, and applications in string theory, including T-duality, generalized geometry, and compactifications.

Contribution

It offers a clear, structured introduction to DFT, covering its formulation, geometric aspects, and connections to supergravity and flux compactifications, with extensions to U-duality.

Findings

DFT incorporates T-duality as a symmetry of a field theory.

Generalized diffeomorphisms and invariant actions are constructed on double space.

Connections between DFT, gauged supergravity, and flux compactifications are established.

Abstract

Double Field Theory (DFT) is a proposal to incorporate T-duality, a distinctive symmetry of string theory, as a symmetry of a field theory defined on a double configuration space. The aim of this review is to provide a pedagogical presentation of DFT and its applications. We first introduce some basic ideas on T-duality and supergravity in order to proceed to the construction of generalized diffeomorphisms and an invariant action on the double space. Steps towards the construction of a geometry on the double space are discussed. We then address generalized Scherk-Schwarz compactifications of DFT and their connection to gauged supergravity and flux compactifications. We also discuss U-duality extensions, and present a brief parcours on world-sheet approaches to DFT. Finally, we provide a summary of other developments and applications that are not discussed in detail in the review.