Holographic Proof of the Quantum Null Energy Condition

TL;DR

This paper proves the Quantum Null Energy Condition (QNEC) for a broad class of theories using holography, establishing it as a fundamental quantum field theory principle and extending previous proofs beyond free theories.

Contribution

The authors provide a holographic proof of the QNEC at leading order in large-N for CFTs with Einstein gravity duals, generalizing previous results to interacting theories.

Findings

QNEC holds for CFTs with Einstein gravity duals in Minkowski space.

The proof extends to relevant deformations of CFTs.

Supports the universality of QNEC in quantum field theories.

Abstract

We use holography to prove the Quantum Null Energy Condition (QNEC) at leading order in large-$N$ for CFTs and relevant deformations of CFTs in Minkowski space which have Einstein gravity duals. Given any codimension-2 surface $\Sigma$ which is locally stationary under a null deformation in the direction $k$ at the point $p$, the QNEC is a lower bound on the energy-momentum tensor at $p$ in terms of the second variation of the entropy to one side of $\Sigma$: $\langle T_{kk}\rangle \geq S"/2\pi \sqrt{h}$. In a CFT, conformal transformations of this inequality give results which apply when $\Sigma$ is not locally stationary. The QNEC was proven previously for free theories, and taken together with our result this provides strong evidence that the QNEC is a true statement about quantum field theory in general.