2019/12/31 by Felipe Rosso
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Conformal field theory #Conformal map #Conformal symmetry #Cosmology and Gravitation Theories #De Sitter universe #Energy condition #Entropy (arrow of time) #Geometry #Mathematical physics #Mathematics #Minkowski space #Noncommutative and Quantum Gravity Theories #Physics #Quantum #Quantum entanglement #Quantum mechanics #Theoretical physics #Universe #gr-qc #hep-th
paper · pdf · doi:10.1007/jhep03(2020)186
published as JHEP 03 (2020) 186 · 57 pages and 9 figures. v2: references added
openalex publication_date 2020/03/01 · arxiv created 2020/12/23 · arxiv updated 2020/12/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A bstract 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.