Papers › A Renyi Quantum Null Energy Condition: Proof for Free Field Theories
A Renyi Quantum Null Energy Condition: Proof for Free Field Theories
Mudassir Moosa, Pratik Rath, Vincent Paul Su
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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 Sᵣₑₗ(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 Sₙ(ρ||σ), which also measures the distinguishability of two states for arbitrary n∈[1/2,∞). A Renyi QNEC, a positivity condition on the second null shape derivative of Sₙ(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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