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.
Highlights
While the original quantum null energy condition (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
Introduction.—Motivated by features desired when relativistic quantum field theories (QFTs) are coupled to gravity, in Ref. [1], Bousso, Fisher, Liechenauer, and Wall proposed the quantum null energy condition (QNEC), which states that the energy density at a point is bounded below by a second derivative at that point of an appropriate von Neumann entropy
The original conjecture assumed the null congruence to be locally stationary at the desired point p, meaning that the expansion θ and shear σαβ satisfy σαβjp 1⁄4 0 and θjp 1⁄4 θjp 1⁄4 0, where the overdot indicates a derivative with respect to an affine parameter along the generator through p and greek indices ðα; β; γ; ...Þ run over the d − 2 directions associated with the cut of the null congruence at which S00 was computed
Summary
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. 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. [1], Bousso, Fisher, Liechenauer, and Wall proposed the quantum null energy condition (QNEC), which states that the (null) energy density at a point is bounded below by a second derivative at that point of an appropriate von Neumann entropy.
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