Holographic solar systems and hydrogen atoms: non-relativistic physics in AdS and its CFT dual

TL;DR

This paper explores a non-relativistic limit of AdS physics that incorporates curvature effects, revealing connections between spectra, correlation functions, and scattering phases, with applications to Coulomb systems like solar systems and hydrogen atoms.

Contribution

It introduces a novel non-relativistic limit of AdS with curvature effects and links it to CFT spectra and scattering, providing new insights into Coulomb systems in AdS.

Findings

Spectrum determined by scattering phase shifts

Correlation functions proportional to the S-matrix

Resonances significantly affect spectra and correlations

Abstract

We study a non-relativistic limit of physics in AdS which retains the curvature through a harmonic Newtonian potential. This limit appears in a CFT dual through the spectrum of operators of large dimension and correlation functions of those operators with appropriate kinematics. In an additional flat spacetime limit, the spectrum is determined by scattering phase shifts (proportional to anomalous dimensions), and a CFT correlation function is proportional to the S-matrix. In particular, we describe the effect of resonances on the spectrum and correlation functions. As an example, we discuss the Coulomb potential (describing solar systems and hydrogen atoms in AdS) in detail.