Radial cutoffs and holographic entanglement

Abstract

Abstract Tensor networks, T T ¯ $$ T\overline{T} $$ , and broader notions of a holographic principle all motivate the idea that some notion of gravitational holography should persist in the presence of a radial cutoff. But in the absence of time-reflection symmetry, the areas of Hubeny-Rangamani-Takayanagi surfaces anchored to the radial cutoff generally violate strong sub-additivity, even when the associated boundary regions are spacelike separated as defined by both bulk and boundary notions of causality. We thus propose an alternate definition of cutoff-holographic entropy using a restricted maximin prescription anchored to a codimension 2 cutoff surface. For bulk solutions that respect the null energy condition, we show that the resulting areas satisfy SSA, entanglement wedge nesting, and monogamy of mutual information in parallel with cutoff free results in AdS. These results hold even when the cutoff surface fails to be convex.

Keywords

• AdS-CFT Correspondence
• Gauge-gravity correspondence