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.

21 pages, 2 figures; v2 minor improvements, reference added, published version

References in corpus (13)

• Many-Body Physics with Ultracold Gases
• Theory of ultracold Fermi gases
• Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry
• Gravity duals for non-relativistic CFTs
• Nonrelativistic conformal field theories
• Conformality Lost
• On the spectrum of nonrelativistic AdS/CFT
• Anomaly in conformal quantum mechanics: From molecular physics to black holes
• Correlation Functions in Non-Relativistic Holography
• Correlation functions in the non-relativistic AdS/CFT correspondence
• Nonrelativistic inverse square potential, scale anomaly, and complex extension
• Geometry of Schroedinger Space-Times, Global Coordinates, and Harmonic Trapping
• A Model Study of Discrete Scale Invariance and Long-Range Interactions

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