AdS/CFT duality for non-relativistic field theory

TL;DR

This paper establishes a holographic duality between non-relativistic conformal field theories and specific gravitational backgrounds, enabling the study of NRCFTs via AdS/CFT techniques.

Contribution

It formulates a new correspondence linking NRCFTs to AdS backgrounds with a compact lightlike dimension, without requiring non-vacuum energy-momentum sources.

Findings

Reproduces the NRCFT state-operator correspondence using gravity

Shows symmetry breaking from AdS to NRCFT via boundary conditions

Validates the duality through matching scaling dimensions and energy spectra

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.