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

• URL: http://arxiv.org/abs/2007.15025v2
• Date: Tue, 11 Aug 2020 20:30:54 GMT
• Title: A Renyi Quantum Null Energy Condition: Proof for Free Field Theories
• Authors: Mudassir Moosa, Pratik Rath, Vincent Paul Su
• Abstract summary: The Quantum Null Energy Condition (QNEC) is a lower bound on the stress-energy tensor in quantum field theory. We study the Renyi QNEC for free and superrenormalizable field theories in spacetime dimension $d>2$ using the technique of null quantization.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $n<1$.

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