Schrödinger Manifolds

Abstract

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.

42 pages, 1 figure, published version: J. Phys. A: Math. Theor. 45 (2012) 395203 (24pp)

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• Non-relativistic conformal symmetries and Newton-Cartan structures
• The geometry of Schrödinger symmetry in non-relativistic CFT
• Geometry of Schroedinger Space-Times, Global Coordinates, and Harmonic Trapping
• Topics in conformally compact Einstein metrics
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