论文标题
renyi量子零能条件：自由场理论的证明
A Renyi Quantum Null Energy Condition: Proof for Free Field Theories
论文作者
论文摘要
量子无效状态（QNEC）是量子场理论中应力能量张量的下限，已被证明是相当普遍的。它可以等效地作为对相对熵$ s _ {\ text {rel}}}（ρ||σ）$ $ρ$相对于真空$ $σ$的相对熵$ s _ {\ text {rel}} $的阳性条件。相对熵具有自然的单参数概括，夹心的renyi Divergence $ s_n（ρ||σ）$，这也测量了两个状态对于[1/2，\ infty）$的两种状态的区分性。在先前的工作中猜想了$ s_n（ρ||σ）$的第二个空形导数（ρ||σ）$的阳性条件的Renyi Qnec。在这项工作中，我们使用零量化技术研究了时空维度$ d> 2 $的免费和超肾小管实地理论的Renyi QNEC。在上述情况下，我们在任意状态的情况下证明了Renyi QNEC $ n> 1 $。我们还以$ n <1 $的价格为Renyi QNEC提供反例。
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 $n<1$.
