Remarks on the non-Riemannian sector in Double Field Theory

초록

Taking O(D,D) 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, (n,n over bar ). Such non-Riemannian backgrounds render a propagating string chiral and anti-chiral over n and n over bar 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 (n,n over bar non-Riemannian sector. We recognize a nontrivial subtlety for nn over bar not equal 0 that infinitesimal variations generically include those which change (n,n over bar ). 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.

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