A Rényi quantum null energy condition: proof for free field theories

DOI10.1007/JHEP01(2021)064zbMATH Open1459.81099arXiv2007.15025OpenAlexW3118328087MaRDI QIDQ2024235

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Publication date: 3 May 2021

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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 $S_{extrel}(ho||sigma)$ of an arbitrary state $ho$ with respect to the vacuum $sigma$. The relative entropy has a natural one-parameter family generalization, the Sandwiched Renyi divergence $S_n(ho||sigma)$, which also measures the distinguishability of two states for arbitrary $nin[1/2,infty)$. A Renyi QNEC, a positivity condition on the second null shape derivative of $S_n(ho||sigma)$, 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 $n<1$.

Full work available at URL: https://arxiv.org/abs/2007.15025

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