Asymptotic symmetry of geometries with Schrodinger isometry

TL;DR

The paper addresses how to realize the infinite-dimensional extension of the Schrödinger symmetry as an asymptotic symmetry of geometries with Schrödinger isometry. By analyzing metrics asymptotically equivalent to Schrödinger backgrounds, it constructs Brown–Henneaux–like boundary conditions and explicit asymptotic Killing vectors that generate an infinite set of charges $L_n$, $Q_{i\hat n}$, and $T_n$, closing the algebra with a Virasoro subalgebra in any dimension. The results show that the asymptotic symmetry algebra contains a Virasoro factor and discuss central extensions, with $d=1$ potentially yielding two Virasoro algebras, aligning with non-relativistic AdS/CFT expectations. This supports gravity dual descriptions of non-relativistic CFTs and clarifies how the $SL(2,\mathbb{R})$ structure within the Schrödinger group underpins the infinite-dimensional symmetry.

Abstract

We show that the asymptotic symmetry algebra of geometries with Schrodinger isometry in any dimension is an infinite dimensional algebra containing one copy of Virasoro algebra. It is compatible with the fact that the corresponding geometries are dual to non-relativistic CFTs whose symmetry algebra is the Schrodinger algebra which admits an extension to an infinite dimensional symmetry algebra containing a Virasoro subalgebra.