Dynamics of Perturbations in Double Field Theory & Non-Relativistic String Theory

TL;DR

This paper demonstrates that non-Riemannian backgrounds in Double Field Theory naturally describe non-relativistic string theories, providing a new geometric framework and analyzing perturbations with a novel formalism.

Contribution

It establishes the equivalence between Gomis-Ooguri non-relativistic string theory and Double Field Theory on non-Riemannian backgrounds, and develops a semi-covariant perturbation formalism.

Findings

Double Field Theory reproduces Gomis-Ooguri string spectrum.

Derived linearized equations of motion for perturbations.

Presented a new non-Riemannian solution with Schrödinger symmetry.

Abstract

Double Field Theory provides a geometric framework capable of describing string theory backgrounds that cannot be understood purely in terms of Riemannian geometry -- not only globally (`non-geometry'), but even locally (`non-Riemannian'). In this work, we show that the non-relativistic closed string theory of Gomis and Ooguri [1] arises precisely as such a non-Riemannian string background, and that the Gomis-Ooguri sigma model is equivalent to the Double Field Theory sigma model of [2] on this background. We further show that the target-space formulation of Double Field Theory on this non-Riemannian background correctly reproduces the appropriate sector of the Gomis-Ooguri string spectrum. To do this, we develop a general semi-covariant formalism describing perturbations in Double Field Theory. We derive compact expressions for the linearized equations of motion around a generic on-shell background, and construct the corresponding fluctuation Lagrangian in terms of novel completely covariant second order differential operators. We also present a new non-Riemannian solution featuring Schr\"odinger conformal symmetry.