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

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.