Below the Breitenlohner-Freedman bound in the nonrelativistic AdS/CFT correspondence

TL;DR

This paper challenges the existence of a stability bound for scalar fields in nonrelativistic AdS/CFT, linking it to quantum mechanics phenomena and providing new insights into holographic renormalization.

Contribution

It demonstrates the absence of a Breitenlohner-Freedman bound in nonrelativistic AdS/CFT and connects scalar field stability to inverse square potentials and quantum limit cycles.

Findings

Two-point correlation functions for m^2<m_{BF}^2 are computed.

The relation to Efimov effect and RG limit cycles is discussed.

Holographic RG flows are elucidated using the equivalence with Schrödinger equations.

Abstract

We propose that there is no analogue of the Breitenlohner-Freedman stability bound on the mass of a scalar field in the context of the nonrelativistic AdS/CFT correspondence. Our treatment is based on an equivalence between the field equation of a complex scalar in the AdS/CFT correspondence and the one-dimensional Schroedinger equation with an inverse square potential. We compute the two-point boundary correlation function for m^2<m_{BF}^2 and discuss its relation to renormalization group limit cycles and the Efimov effect in quantum mechanics. The equivalence also helps to elucidate holographic renormalization group flows and calculations in the global coordinates for Schroedinger spacetime.