Bulk Matter and the Boundary Quantum Null Energy Condition

TL;DR

This paper explores the quantum null energy condition (QNEC) in holographic conformal field theories, revealing saturation in higher dimensions and new implications for bulk energy conditions when matter is present.

Contribution

It provides direct calculations of entanglement entropy variations and establishes new bulk energy conditions derived from QNEC in holographic settings.

Findings

QNEC is saturated in dimensions greater than 2.

In 2D, QNEC is generally not saturated with bulk matter.

New bulk energy conditions stronger than the averaged null energy condition are derived.

Abstract

We investigate the quantum null energy condition (QNEC) in holographic CFTs, focusing on half-spaces and particular classes of states. We present direct, and in certain cases nonperturbative, calculations for both the diagonal and off- diagonal variational derivatives of entanglement entropy. In d > 2, we find that the QNEC is saturated. We compute relations between the off-diagonal variation of entanglement, boundary relative entropy, and the bulk stress tensor. Strong subadditivity then leads to energy conditions in the bulk. In d = 2, we find that the QNEC is in general not saturated when the Ryu-Takayanagi surface intersects bulk matter. Moreover, when bulk matter is present the QNEC can imply new bulk energy conditions. For a simple class of states, we derive an example that is stronger than the bulk averaged null energy condition and reduces to it in certain limits.