Constructing entanglement wedges for Lifshitz spacetimes with Lifshitz gravity

Abstract

Holographic relationships between entanglement entropy on the boundary of a spacetime and the area of minimal surfaces in the bulk provide an important entry in the bulk/boundary dictionary. While constructing the necessary causal and entanglement wedges is well understood in asymptotically AdS spacetimes, less is known about the equivalent constructions in spacetimes with different asymptotics. In particular, recent attempts to construct entanglement and causal wedges for asymptotically Lifshitz solutions in relativistic gravitational theories have proven problematic. We note a simple observation, that a Lifshitz bulk theory, specifically a covariant formulation of Hořava-Lifshitz gravity coupled to matter, has causal propagation defined by Lifshitz modes. We use these modes to construct causal and entanglement wedges and compute the geometric entanglement entropy, which in such a construction matches the field theory prescription.

arXiv comment7 pages, 2 figures

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Cited by in corpus (6)

• Warped Information and Entanglement Islands in AdS/WCFT
• Entanglement Evolution in Lifshitz-type Scalar Theories
• Hawking Radiation from Universal Horizons
• Informational properties of holographic Lifshitz field theory
• Entanglement wedge method, out-of-time-ordered correlators, and pole skipping
• Energy-entropy relation for asymptotically Lifshitz spacetimes with universal horizons