On the spectrum of nonrelativistic AdS/CFT

TL;DR

This paper develops a Hamiltonian framework for nonrelativistic AdS/CFT models, connecting holographic descriptions with many-body fermion spectra and exploring physical implications like mass gaps and phase transitions.

Contribution

It introduces a Hamiltonian approach to nonrelativistic AdS/CFT, enabling direct comparison with many-body fermion spectra and physical interpretation of the holographic coordinate.

Findings

Exact AdS metrics can realize physical requirements without exotic matter.

The holographic radial coordinate correlates with many-body spectra.

Speculations on mass gap generation and phase transitions in the AdS context.

Abstract

We develop a Hamiltonian picture for a family of models of nonrelativistic AdS/CFT duality. The Schrodinger group is realized via the conformal quantum mechanics of De Alfaro, Fubini and Furlan in the holographic direction. We show that most physical requirements, including the introduction of harmonic traps, can be realized with exact AdS metrics, but without any need for exotic matter sectors in the bulk dynamics. This Hamiltonian picture can be used to compare directly with many-body spectra of fermions at unitarity on harmonic traps, thereby providing a direct physical interpretation of the holographic radial coordinate for these systems. Finally, we add some speculations on the dynamical generation of mass gaps in the AdS description, the resulting quasiparticle spectra, and the analog of `deconfining' phase transitions that may occur.