String Theory and non-Riemannian Geometry

TL;DR

This paper explores non-Riemannian geometries in string theory using an $ extbf{O}(D,D)$ covariant framework, revealing anomaly-free vacua with unique spectra that could suggest new compactification methods.

Contribution

It introduces non-Riemannian backgrounds in string theory, quantizes strings on these backgrounds, and finds consistent, anomaly-free vacua with spectra matching Double Field Theory.

Findings

Identified flat, anomaly-free non-Riemannian string vacua in critical dimensions.

The string spectrum is restricted to one level with no tachyon.

Spectrum matches linearized equations of Double Field Theory.

Abstract

The $\mathbf{O}(D,D)$ covariant generalized metric, postulated as a truly fundamental variable, can describe novel geometries where the notion of Riemannian metric ceases to exist. Here we quantize a closed string upon such backgrounds and identify flat, anomaly-free, non-Riemannian string vacua in the familiar critical dimension, $D{=26}$ (or $D{=10}$). Remarkably, the whole BRST closed string spectrum is restricted to just one level with no tachyon, and matches the linearized equations of motion of Double Field Theory. Taken as an internal space, our non-Riemannian vacua may open up novel avenues alternative to traditional string compactification.