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

Journal Article · Wed Jan 13 00:00:00 EST 2021 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep01(2021)064· OSTI ID:1798154

Moosa, Mudassir  ^[1]; Rath, Pratik ^[2]; Su, Vincent Paul ^[2]

---

1. Cornell Univ., Ithaca, NY (United States)
2. Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

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_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 Rényi divergence S_n(ρ||σ), which also measures the distinguishability of two states for arbitrary n ∈ [1/2, ∞). A Rényi 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 Rényi 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 Rényi QNEC in the case n > 1 for arbitrary states. We also provide counterexamples to the Rényi QNEC for n < 1.

• Research Organization: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
• Sponsoring Organization: USDOE Office of Science (SC)
• Grant/Contract Number: AC02-05CH11231
• OSTI ID: 1798154
• Journal Information: Journal of High Energy Physics (Online), Vol. 2021, Issue 1; ISSN 1029-8479
• Publisher: Springer Berlin
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS