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arXiv 2007.15025hep-thgr-qcquant-ph
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一个Renyi量子能量条件：自由场论的证明

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

Mudassir Moosa, Pratik Rath, Vincent Paul Su

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39 pages, 6 figures
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摘要：

量子场论能量条件（QNEC）是量子场论中应力-能量张量的一个下界，已经得到了相当普遍的证明。它可以等价地表述为任意态$ρ$相对于真空$σ$的相对熵$S_{\text{rel}}(ρ||σ)$的二阶零形导数的正性条件。相对熵有一个自然的单参数族推广，三明治Renyi分歧$S_n(ρ||σ)$，它也衡量了两个国家的任意$n\in[1/2,\infty)$的可扩展性。在以前的工作中，我们证明了$S_n(ρ||σ)$的二阶零形导数的一个正性条件Renyi QNEC。本文利用零量子化技术研究了时空维$d>2$中自由和超重整化场论的Renyi QNEC。在上面的设置中，我们证明了Renyi QNEC的情况下，$n>1$的任意状态。我们还提供了$n<1$的Renyi QNEC的反例。

英文摘要：

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 $S_{\text{rel}}(ρ||σ)$ of an arbitrary state $ρ$ with respect to the vacuum $σ$. The relative entropy has a natural one-parameter family generalization, the Sandwiched Renyi divergence $S_n(ρ||σ)$, 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 $S_n(ρ||σ)$, 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 $n<1$.

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