Examinando por Autor "Morand, K."

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  • Miniatura
    Ítem
    Classification of non-Riemannian doubled-yet-gauged spacetime
    (Springer New York LLC, 2017-10) Morand, K.; Park, J.-H.
    Assuming O(D, D) covariant fields as the ‘fundamental’ 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¯) , 0 ≤ n+ n¯ ≤ D. Upon these backgrounds, strings become chiral and anti-chiral over n and n¯ directions, respectively, while particles and strings are frozen over the n+ 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’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 spacetime such as D= 10 , (3, 3) may open a new scheme for the dimensional reduction from ten to four. © 2017, The Author(s).
  • Miniatura
    Ítem
    Connections and dynamical trajectories in generalised Newton-Cartan gravity. II. An ambient perspective
    (American Institute of Physics Inc., 2018-07) Bekaert, X.; Morand, K.
    Connections compatible with degenerate metric structures are known to possess peculiar features: on the one hand, the compatibility conditions involve restrictions on the torsion; on the other hand, torsionfree compatible connections are not unique, the arbitrariness being encoded in a tensor field whose type depends on the metric structure. Nonrelativistic structures typically fall under this scheme, the paradigmatic example being a contravariant degenerate metric whose kernel is spanned by a one-form. Torsionfree compatible (i.e., Galilean) connections are characterised by the gift of a two-form (the force field). Whenever the two-form is closed, the connection is said Newtonian. Such a nonrelativistic spacetime is known to admit an ambient description as the orbit space of a gravitational wave with parallel rays. The leaves of the null foliation are endowed with a nonrelativistic structure dual to the Newtonian one, dubbed Carrollian spacetime. We propose a generalisation of this unifying framework by introducing a new non-Lorentzian ambient metric structure of which we study the geometry. We characterise the space of (torsional) connections preserving such a metric structure which is shown to project to (respectively, embed) the most general class of (torsional) Galilean (respectively, Carrollian) connections. © 2018 Author(s).