Losing the IR: a Holographic Framework for Area Theorems

TL;DR

This paper introduces a holographic framework that explains gravitational area laws as arising from ignorance of infrared data in the dual CFT, linking them to entropy inequalities and extending to quantum corrections.

Contribution

It provides a precise holographic framework connecting bulk area laws to boundary entropy properties, including mixed signatures and quantum corrections.

Findings

Boundary dual to area laws is strong subadditivity of von Neumann entropy.

Framework explains mixed signature area laws.

Inclusion of quantum corrections leads to generalized second laws.

Abstract

Gravitational area laws are expected to arise as a result of ignorance of "UV gravitational data". In AdS/CFT, the UV/IR correspondence suggests that this data is dual to infrared physics in the CFT. Motivated by these heuristic expectations, we define a precise framework for explaining bulk area laws (in any dimension) by discarding IR CFT data. In (1+1) boundary dimensions, our prescribed mechanism shows explicitly that the boundary dual to these area laws is strong subadditivity of von Neumann entropy. Moreover, such area laws may be of arbitrary (and mixed) signature; thus our framework gives the first entropic explanation of mixed signature area laws (as well as area laws for certain dynamical causal horizons). In general dimension, the framework is easily modified to include bulk quantum corrections, thus giving rise to an infinite family of bulk generalized second laws.