A Renyi Quantum Null Energy Condition: Proof for Free Field Theories

TL;DR

This paper proves the Renyi Quantum Null Energy Condition (QNEC) for free and superrenormalizable field theories in higher dimensions for certain parameters, extending the understanding of quantum energy bounds.

Contribution

It provides the first proof of the Renyi QNEC for free field theories for n>1, and shows counterexamples for n<1, advancing quantum energy condition research.

Findings

Proved Renyi QNEC for n>1 in free field theories.

Counterexamples to Renyi QNEC for n<1.

Extended quantum energy bounds to a broader class of theories.

Abstract

The Quantum Null Energy Condition (QNEC) is a lower bound on the stress-energy tensor in quantum field theory that has been proved quite generally. It can equivalently be phrased as a positivity condition on the second null shape derivative of the relative entropy $S_{\text{rel}}(\rho||\sigma)$ of an arbitrary state $\rho$ with respect to the vacuum $\sigma$. The relative entropy has a natural one-parameter family generalization, the Sandwiched Renyi divergence $S_n(\rho||\sigma)$, which also measures the distinguishability of two states for arbitrary $n\in[1/2,\infty)$. A Renyi QNEC, a positivity condition on the second null shape derivative of $S_n(\rho||\sigma)$, was conjectured in previous work. In this work, we study the Renyi QNEC for free and superrenormalizable field theories in spacetime dimension $d>2$ using the technique of null quantization. In the above setting, we prove the Renyi QNEC in the case $n>1$ for arbitrary states. We also provide counterexamples to the Renyi QNEC for $n<1$.