Global aspects of conformal symmetry and the ANEC in dS and AdS

TL;DR

This paper demonstrates that conformal symmetry enforces the averaged null energy condition (ANEC) in de Sitter and anti-de Sitter spacetimes, using multiple methods including entropy and causality arguments, with implications for holography.

Contribution

It introduces novel bounds for the ANEC in (A)dS and the cylinder, derived through symmetry, entropy, and causality, extending the understanding of energy conditions in conformal field theories.

Findings

ANEC holds in (A)dS and cylindrical backgrounds due to conformal symmetry.

Vacuum modular Hamiltonian and entanglement entropy are obtained for null deformed regions.

Rindler positivity extends to conformal theories in (A)dS and the cylinder.

Abstract

Starting from the averaged null energy condition (ANEC) in Minkowski we show that conformal symmetry implies the ANEC for a conformal field theory (CFT) in a de Sitter and anti-de Sitter background. A similar and novel bound is also obtained for a CFT in the Lorentzian cylinder. Using monotonicity of relative entropy, we rederive these results for dS and the cylinder. As a byproduct we obtain the vacuum modular Hamiltonian and entanglement entropy associated to null deformed regions of CFTs in (A)dS and the cylinder. A third derivation of the ANEC in dS is shown to follow from bulk causality in AdS/CFT. Finally, we use the Tomita-Takesaki theory to show that Rindler positivity of Minkowski correlators generalizes to conformal theories defined in dS and the cylinder.