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.
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ArXiv ePrint: 1912.08897
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Rosso, F. Global aspects of conformal symmetry and the ANEC in dS and AdS. J. High Energ. Phys. 2020, 186 (2020). https://doi.org/10.1007/JHEP03(2020)186
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DOI: https://doi.org/10.1007/JHEP03(2020)186