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
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Accepted: 13 January 2020
Published online: 6 February 2020
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.
© The Author(s), 2020