Eur. Phys. J. C (2020) 80: 101
https://doi.org/10.1140/epjc/s10052-020-7648-9

Regular Article - Theoretical Physics

Remarks on the non-Riemannian sector in Double Field Theory

Department of Physics, Sogang University, 35 Baekbeom-ro, Mapo-gu, Seoul, 04107, Korea

^* e-mail: park@sogang.ac.kr

Received: 2 October 2019
Accepted: 13 January 2020
Published online: 6 February 2020

Abstract

Taking covariant field variables as its truly fundamental constituents, Double Field Theory can accommodate not only conventional supergravity but also non-Riemannian gravities that may be classified by two non-negative integers, . Such non-Riemannian backgrounds render a propagating string chiral and anti-chiral over n and dimensions respectively. Examples include, but are not limited to, Newton–Cartan, Carroll, or Gomis–Ooguri. Here we analyze the variational principle with care for a generic non-Riemannian sector. We recognize a nontrivial subtlety for that infinitesimal variations generically include those which change . This seems to suggest that the various non-Riemannian gravities should better be identified as different solution sectors of Double Field Theory rather than viewed as independent theories. Separate verification of our results as string worldsheet beta-functions may enlarge the scope of the string landscape far beyond Riemann.