String Theory and non-Riemannian Geometry

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.

arXiv comment6 pages. [v2] comment/reference added, title changed from "Single Level String Theory", to appear in PRL

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Cited by in corpus (19)

• Aspects of Nonrelativistic Strings
• Torsional string Newton-Cartan geometry for non-relativistic strings
• A Non-Relativistic Limit of NS-NS Gravity
• Non-Relativistic Ten-Dimensional Minimal Supergravity
• Nonrelativistic Approximations of Closed Bosonic String Theory
• Non-Riemannian isometries from double field theory
• Non-Riemannian gravity actions from double field theory
• Non-abelian U-duality at work
• Fractons, non-Riemannian Geometry, and Double Field Theory
• Identifying Riemannian singularities with regular non-Riemannian geometry
• Post-Newtonian Feasibility of the Closed String Massless Sector
• Double Field Theory and Geometric Quantisation
• Type II Double Field Theory in Superspace
• Notes on Ramond-Ramond spinors and bispinors in double field theory
• Traversable wormhole for string, but not for particle
• Gravitational Core of Double Field Theory: Lecture Notes
• Late-time Cosmology without Dark Sector but with Closed String Massless Sector
• Universal Box Operator: $\mathbf{O}(D,D)$-Symmetry and ${\alpha }^{\prime }$-Corrections
• Extended Field Theories as higher Kaluza-Klein theories