Modular Hamiltonian for de Sitter diamonds

Abstract

We determine the Tomita-Takesaki modular data for CFTs in double cone and light cone regions in conformally flat spacetimes. This includes in particular the modular Hamiltonian for diamonds in the de Sitter spacetime. In the limit where the diamonds become large, we show that the modular automorphisms become time translations in the static patch. As preparation, we also provide a pedagogical rederivation of the known results for Minkowski spacetime. With our results and using the Araki formula, it becomes possible to compute relative entanglement entropies for CFTs in these regions.

58 pages, 10 figures. Matches published version

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Cited by in corpus (6)

• Entropy-area law and temperature of de Sitter horizons from modular theory
• Modular Fluctuations in Cosmology
• Quantum information and the C-theorem in de Sitter
• Modular Hamiltonian for fermions of small mass
• Notions of Fermionic Entropies of a Causal Fermion System
• The Sine-Gordon QFT in de Sitter spacetime