Gravitational Core of Double Field Theory: Lecture Notes

TL;DR

This paper introduces Double Field Theory as a promising alternative to General Relativity, emphasizing its symmetry principles and potential to address unresolved gravitational questions.

Contribution

It provides an accessible, structured overview of DFT, highlighting its foundational concepts, mathematical framework, and its role as a unified field theory for string massless sectors.

Findings

DFT offers a covariant framework with doubled coordinates.

It generalizes Einstein's equations with $ extbf{O}(D,D)$ symmetry.

DFT addresses unresolved issues in classical gravity.

Abstract

Double Field Theory (DFT) has emerged as a comprehensive framework for gravity, presenting a testable and robust alternative to General Relativity (GR), rooted in the $\mathbf{O}(D,D)$ symmetry principle of string theory. These lecture notes aim to provide an accessible introduction to DFT, structured in a manner similar to traditional GR courses. Key topics include doubled-yet-gauged coordinates, Riemannian versus non-Riemannian parametrisations of fundamental fields, covariant derivatives, curvatures, and the $\mathbf{O}(D,D)$-symmetric augmentation of the Einstein field equation, identified as the unified field equation for the closed string massless sector. By offering a novel perspective, DFT addresses unresolved questions in GR and enables the exploration of diverse physical phenomena, paving the way for significant future research.