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

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.

57 pages and 9 figures. v2: references added

References in corpus (8)

• Towards a derivation of holographic entanglement entropy
• Conformal collider physics: Energy and charge correlations
• Holographic c-theorems in arbitrary dimensions
• Achronal averaged null energy condition
• A holographic proof of the averaged null energy condition
• Averaged null energy condition in a classical curved background
• Conformally invariant averaged null energy condition from AdS/CFT
• Rényi mutual information inequalities from Rindler positivity

Cited by in corpus (8)

• Lightcone Commutator and Stress-Tensor Exchange in $d>2$ CFTs
• Quantum BMS transformations in conformally flat space-times and holography
• A Generalized Nachtmann Theorem in CFT
• Achronal averaged null energy condition for extremal horizons and (A)dS
• The averaged null energy condition on holographic evaporating black holes
• The averaged null energy conditions in even dimensional curved spacetimes from AdS/CFT duality
• Endpoint contributions to excited-state modular Hamiltonians
• Light-ray moments as endpoint contributions to modular Hamiltonians