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

• Published in: The journal of high energy physics Vol. 2021; no. 1; pp. 1 - 49
• Main Authors: Moosa, Mudassir, Rath, Pratik, Su, Vincent Paul
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 13-01-2021; Springer Nature B.V; Springer Berlin; SpringerOpen
• Subjects: Classical and Quantum Gravitation; Conformal Field Theory; Elementary Particles; Entropy; Field Theories in Higher Dimensions; Field theory; High energy physics; Lower bounds; Physics; Physics and Astronomy; PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Quantum theory; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Tensors; Conformal Field Theory; Field Theories in Higher Dimensions
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP01(2021)064

A
bstract
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.