Scalar Boundary Conditions in Lifshitz Spacetimes

Abstract

We investigate the conditions imposable on a scalar field at the boundary of the so- called Lifshitz spacetime which has been proposed as the dual to Lifshitz field theories. For effective mass squared between -(d+z-1)^2/4 and z^2-(d+z-1)^2/4, we find a one-parameter choice of boundary condition type. The bottom end of this range corresponds to a Breitenlohner-Freedman bound; below it, the Klein-Gordon operator need not be positive, so we cannot make sense of the dynamics. Above the top end of the range, only one boundary condition type is available; here we expect compact initial data will remain compact in the future.

references added

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Cited by in corpus (2)

• Boundary Stress-Energy Tensor and Newton-Cartan Geometry in Lifshitz Holography
• Holographic quantum critical points in Lifshitz space-time