On the spectrum of nonrelativistic AdS/CFT

TL;DR

This work develops a Hamiltonian picture for nonrelativistic AdS/CFT (NR AdS/CFT), showing that Schrödinger symmetry can be realized by conformal quantum mechanics in the holographic direction and that exact AdS metrics suffice without exotic bulk matter. It provides a concrete bulk-to-boundary dictionary: the radial coordinate acts as a collective radial mode with a conformal quantum-mechanical sector, and harmonic trapping translates into a geometrical mechanism that yields a discrete spectrum and direct links to conformal dimensions. A key contribution is the precise matching to fermions at unitarity in harmonic traps, mapping the trapped many-body spectrum to bulk mass data and revealing a Breitenlohner–Freedman bound as a physical constraint on admissible internal spectra. The work also explores mass-gap generation and quasiparticle towers via radial deformations, offering thermodynamic implications akin to extra dimensions and outlining future directions toward string embeddings and deconfinement-type transitions.

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.

Figures (1)

• Figure 1: Plots of the potential $U(\rho) = \frac{b}{2M\rho^2} + v(\rho)$ that one can induce on the holographic radial coordinate $\rho$ to model the generation of a mass gap. The red line presents the conformal potential, with vanishing $v(\rho)$, while the blue line represents the potential with non-zero $v(\rho)$. On the left plot we have the harmonic deformation, $v(\rho) = \frac{1}{2} M \Omega_\rho^2 \rho^2$, while on the right we add a sharp wall of finite or infinite height.