Classification of non-Riemannian doubled-yet-gauged spacetime

Abstract

Assuming O(D, D) covariant fields as the &apos;fundamental&apos; variables, double field theory can accommodate novel geometries where a Riemannian metric cannot be defined, even locally. Here we present a complete classification of such non-Riemannian spacetimes in terms of two non-negative integers, (n,(n) over bar), 0 <= n + (n) over bar <= D. Upon these backgrounds, strings become chiral and anti-chiral over n and (n) over bar directions, respectively, while particles and strings are frozen over the n + (n) over bar n directions. In particular, we identify (0, 0) as Riemannian manifolds, (1, 0) as non-relativistic spacetime, (1, 1) as Gomis-Ooguri non-relativistic string, (D-1, 0) as ultra-relativistic Carroll geometry, and (D, 0) as Siegel&apos;s chiral string. Combined with a covariant Kaluza-Klein ansatz which we further spell, (0, 1) leads to Newton-Cartan gravity. Alternative to the conventional string compactifications on small manifolds, non-Riemannian space-time such as D = 10, (3, 3) may open a new scheme for the dimensional reduction from ten to four © The Author(s) 2017.