Bare Quantum Null Energy Condition

TL;DR

This paper investigates the quantum null energy condition (QNEC) for unrenormalized quantities, extending its applicability beyond previously known cases and relating it to the quantum focusing conjecture in semiclassical gravity.

Contribution

It introduces a generalized form of the QNEC applicable to bare, unrenormalized quantities, connecting it to the quantum focusing conjecture in semiclassical gravity.

Findings

Bare QNEC can hold even when divergences do not cancel.

The quantum focusing conjecture is a special case of the bare QNEC.

The study extends the validity of QNEC to more general quantum field theory contexts.

Abstract

The quantum null energy condition (QNEC) is a conjectured relation between a null version of quantum field theory energy and derivatives of quantum field theory von Neumann entropy. In some cases, divergences cancel between these two terms and the QNEC is intrinsically finite. We study the more general case here where they do not and argue that a QNEC can still hold for bare (unrenormalized) quantities. While the original QNEC applied only to locally stationary null congruences in backgrounds that solve semiclassical theories of quantum gravity, at least in the formal perturbation theory at a small Planck length, the quantum focusing conjecture can be viewed as the special case of our bare QNEC for which the metric is on shell.