AdS/CFT duality for non-relativistic field theory

TL;DR

The paper develops a holographic framework linking non-relativistic conformal field theories in d−1 spatial dimensions to gravity in AdS$_{d+2}$ with a compact lightlike direction, achieving Schrödinger symmetry through boundary conditions. It extends the AdS/CFT dictionary to NRCFTs by correlating boundary primary operators of definite particle number with bulk fields carrying null momentum, and derives NRCFT correlators that match Schrödinger-invariant forms. The global (time) structure is treated via an oscillator-like Hamiltonian $H_o=H+ extomega^2 C$, reproducing the state-operator correspondence and yielding a unitarity bound on scaling dimensions from bulk normalizability. The work provides a self-contained, semiclassical AdS/NRCFT dictionary and discusses extensions to finite temperature/density, supersymmetric realizations, and additional bulk fields to capture a fuller operator spectrum.

Abstract

We formulate a correspondence between non-relativistic conformal field theories (NRCFTs) in d-1 spatial dimensions and gravitational theories in AdS_{d+2} backgrounds with one compactified lightlike direction. The breaking of the maximal SO(2,d+1) symmetry of AdS_{d+2} to the non-relativistic conformal group arises from boundary conditions on bulk fields, without the need to introduce non-vacuum sources of energy-momentum. As a check of the proposal, we use the gravitational theory to reproduce the NRCFT state-operator correspondence between scaling dimensions of primary operators and energy eigenstates of the non-relativistic system placed in an external harmonic potential.