Freedom near Lightcone and ANEC Saturation

TL;DR

This paper explores the saturation of Averaged Null Energy Conditions (ANECs) in conformal field theories and holography, revealing a unique near-lightcone behavior of thermal stress-tensor correlators when ANECs are saturated.

Contribution

It demonstrates that ANEC saturation implies the vanishing of higher-spin stress tensor contributions and results in vacuum-like thermal correlators near the lightcone.

Findings

ANEC saturation coincides with superluminal signals in holography.

Higher-spin operators also saturate ANECs at the same point.

Thermal correlators become vacuum-like near the lightcone when ANECs are saturated.

Abstract

Averaged Null Energy Conditions (ANECs) hold in unitary quantum field theories. In conformal field theories, ANECs in states created by the application of the stress tensor to the vacuum lead to three constraints on the stress-tensor three-point couplings, depending on the choice of polarization. The same constraints follow from considering two-point functions of the stress tensor in a thermal state and focusing on the contribution of the stress tensor in the operator product expansion (OPE). One can observe this in holographic Gauss-Bonnet gravity, where ANEC saturation coincides with the appearance of superluminal signal propagation in thermal states. We show that, when this happens, the corresponding generalizations of ANECs for higher-spin multi-stress tensor operators with minimal twist are saturated as well and all contributions from such operators to the thermal two-point functions vanish in the lightcone limit. This leads to a special near-lightcone behavior of the thermal stress-tensor correlators -- they take the vacuum form, independent of temperature.