Proof of Renyi QNEC for free fermions

TL;DR

This paper proves the Renyi quantum null energy condition (QNEC) for free fermionic quantum field theories in higher dimensions using null quantization, extending the understanding of energy conditions in quantum field theory.

Contribution

It provides the first proof of the Renyi QNEC for free fermions in dimensions greater than two, using null quantization techniques for Renyi parameter n>1.

Findings

Renyi QNEC holds for free fermions in >2 dimensions

Proof applies to Renyi parameter n>1

Uses null quantization method

Abstract

Quantum null energy condition (QNEC) is usually stated as a bound on the expectation value of null components of the stress energy tensor at a point in terms of second null shape variations of the entanglement entropy at the same point. It can be recast as the statement that the sign of the second null shape variation of the relative entropy of any state with respect to the vacuum is positive. Using instead a Renyi generalization of relative entropy, called sandwiched Renyi divergence (SRD), leads to what is termed the Renyi QNEC: the second null shape variation of SRD of any state with respect to the vacuum is positive. In this work, we prove the Renyi QNEC for free and superrenormalizable fermionic quantum field theories in spacetime dimensions greater than 2 using null quantization, for the case where the Renyi parameter $n>1$. We end with comments on multiple possible generalizations.