The geometry of Schr\"odinger symmetry in non-relativistic CFT

TL;DR

This paper explores the geometric structure of Schr"odinger symmetry in non-relativistic conformal field theories using the Bargmann framework, connecting gravity backgrounds, Newton-Hooke symmetries, and hydrodynamical models.

Contribution

It provides a geometric interpretation of Schr"odinger symmetry in non-relativistic CFTs and extends the framework to include Newton-Hooke symmetries and hydrodynamical descriptions.

Findings

Bargmann framework explains Schr"odinger symmetry in gravity backgrounds.

Newton-Hooke conformal symmetries are characterized similarly.

Examples include topologically massive gravity and Madelung hydrodynamics.

Abstract

The non-relativistic conformal "Schroedinger" 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 Schroedinger 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.