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

Understand

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.