Schrödinger Manifolds

Christian Duval (1, 2) , Serge Lazzarini (2, 1)

1 CPT - E2 Géométrie, Physique et Symétries
2 CPT - Centre de Physique Théorique - UMR 7332

This article propounds, in the wake of influential work of Fefferman and Graham about Poincaré extensions of conformal structures, a definition of a (Poincaré-)Schrödinger manifold whose boundary is endowed with a conformal Bargmann structure above a non-relativistic Newton-Cartan spacetime. Examples of such manifolds are worked out in terms of homogeneous spaces of the Schrödinger group in any spatial dimension, and their global topology is carefully analyzed. These archetypes of Schrödinger manifolds carry a Lorentz structure together with a preferred null Killing vector field; they are shown to admit the Schrödinger group as their maximal group of isometries. The relationship to similar objects arising in the non-relativisitc AdS/CFT correspondence is discussed and clarified.

Mots clés: Conformal structures; Fefferman-Graham construction; Schrödinger group; Non-relativistic holography

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Géométrie différentielle [math.DG]; Physique des Hautes Energies - Théorie [hep-th]

Christian Duval, Serge Lazzarini. Schrödinger Manifolds. Journal of Physics A: Mathematical and Theoretical, 2012, 45, pp.395203. ⟨10.1088/1751-8113/45/39/395203⟩. ⟨hal-00656175v5⟩