Radial Cutoffs and Holographic Entanglement

TL;DR

This paper proposes a new approach to defining holographic entanglement entropy with a radial cutoff that preserves key entropic inequalities, addressing issues in non-time-reflection symmetric spacetimes.

Contribution

It introduces a restricted maximin prescription for cutoff-holographic entropy that maintains strong subadditivity and other entropic properties in more general bulk geometries.

Findings

The new prescription satisfies SSA, entanglement wedge nesting, and monogamy of mutual information.

Results hold even when the cutoff surface is non-convex.

Applicable to bulk solutions respecting the null energy condition.

Abstract

Tensor networks, $T\bar{T}$, 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 subadditivity, 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.