Proof of the quantum null energy condition for free fermionic field theories

TL;DR

This paper proves the quantum null energy condition (QNEC) for free fermionic quantum field theories, extending previous proofs that were limited to bosonic theories and stationary null surfaces.

Contribution

It provides the first proof of QNEC for fermionic field theories using similar assumptions and methods as prior bosonic proofs.

Findings

QNEC holds for free fermionic field theories.

The proof extends the validity of QNEC beyond bosonic theories.

The result applies to points on null surfaces in fermionic theories.

Abstract

The quantum null energy condition (QNEC) is a quantum generalization of the null energy condition which gives a lower bound on the null energy in terms of the second derivative of the von Neumann entropy or entanglement entropy of some region with respect to a null direction. The QNEC states that $\langle T_{kk}\rangle_{p}\geq lim_{A\rightarrow 0}\left(\frac{\hbar}{2\pi A}S_{out}^{\prime\prime}\right)$ where $S_{out}$ is the entanglement entropy restricted to one side of a codimension-2 surface $\Sigma$ which is deformed in the null direction about a neighborhood of point $p$ with area $A$. A proof of QNEC has been given before, which applies to free and super-renormalizable bosonic field theories, and to any points that lie on a stationary null surface. Using similar assumptions and methods, we prove the QNEC for fermionic field theories.