Remarks on the non-Riemannian sector in Double Field Theory

Abstract

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). Such non-Riemannian backgrounds render a propagating string chiral and anti-chiral over n andn 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) non-Riemannian sector. We recognize a nontrivial subtlety for nn = 0, which 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. arXiv:1909.10711v1 [hep-th] 24 Sep 2019 1.1 Double Field Theory as the O(D, D) completion of General Relativity While the initial motivation of Double Field Theory was to reformulate supergravity in an O(D, D) manifest manner [2-7] ([58-60] for reviews), through subsequent further developments [61-64], DFT has evolved and can be now identified as Stringy Gravity, i.e. pure gravitational theory that string theory seems to predict foremost. 1 More specifically, DFT is the string theory based, O(D, D) completion of General Relativity: taking the O(D, D) symmetry of string theory as the first principle, this Stringy Gravity assumes the whole massless NS-NS sector of closed string as the fundamental gravitational multiplet and interacts with other superstring sectors (R-R [67-69], R-NS [70], and heterotic Yang-Mills [71-73]). Having said that, regardless of supersymmetry, it can also couple to various matter fields which may appear in lower dimensional effective field theories [70, 74, 75], just as General Relativity (GR) does so. In particular, supersymmetric extensions have been completed to the full (i.e. quartic) order in fermions for D = 10 case 1 At least formally let alone its phenomenological validity, c.f. [65, 66].

Non-relativistic gravity and its coupling to matter

“…This in turn is interesting since the construction of such non-relativistic quantum gravity theories could provide an alternate route towards (relativistic) quantum gravity, as opposed to approaching the latter from either the classical GR or quantum field theory perspective. In fact, the question of a UV completion of non-relativistic gravity theories in terms of non-relativistic string theory has recently received a lot of attention [23-29, 31, 32, 44-47] 3 (see also [46,[50][51][52][53] for a relation to double field theory). Related to this, another relevant application is that classical non-relativistic gravity may have an important role to play in novel types of holographic dualities (see e.g.…”

Reductions of exceptional field theories

“…It would also be interesting to construct explicit solutions using the KK type gauge fields in the reduction along the lines of [59]. The reductions described here might also be useful in relating different non-Riemannian solutions of EFT and DFT following [30] and [60][61][62].…”

Non-Riemannian isometries from double field theory

“…By solving the conditions (1.4) in full generality, a unified description of non-Riemannian parametrisations was then classified in [30]. This was further studied in for instance [31][32][33].…”