The geometry of Schrodinger symmetry in non-relativistic CFT

The non-relativistic conformal Schrodinger symmetry of some gravity backgrounds proposed recently in the AdS/CFT context, is explained in the Bargmann framework. The formalism incorporates the Equivalence Principle. Newton-Hooke conformal symmetries, which are analogs of those of Schrodinger in the presence of a negative cosmological constant, are discussed in a similar way. Further examples include topologically massive gravity with negative cosmological constant and the Madelung hydrodynamical description. (C) 2009 Elsevier Inc. All rights reserved.