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de Sitter entropy from conformal field theory

Daniel Kabat, Gilad Lifschytz

TL;DR

The authors propose that de Sitter space entropy can be understood as the mutual entropy of a dual Euclidean CFT in the dS/CFT framework. They develop a planar-coordinate construction where horizon entropy corresponds to mutual information across a boundary sphere, and show that in a dS3/CFT2 setting the mutual entropy scales with the central charge and the UV cutoff set by the de Sitter scale. Through an analytic continuation from AdS to de Sitter, they relate nonunitarity in the dS CFT and field masses to AdS boundary conditions, and interpret static-coordinate entropy as entanglement across energy scales. They argue that unitary time evolution imposes a fundamental entropy bound tied to $S_{dS}$ and that exceeding this bound signals a phase transition or naked singularity in the AdS picture, thereby linking holographic entanglement, RG flow, and cosmological entropy in a unified framework.

Abstract

We propose that the entropy of de Sitter space can be identified with the mutual entropy of a dual conformal field theory. We argue that unitary time evolution in de Sitter space restricts the total number of excited degrees of freedom to be bounded by the de Sitter entropy, and we give a CFT interpretation of this restriction. We also clarify issues arising from the fact that both de Sitter and anti de Sitter have dual descriptions in terms of conformal field theory.

de Sitter entropy from conformal field theory

TL;DR

The authors propose that de Sitter space entropy can be understood as the mutual entropy of a dual Euclidean CFT in the dS/CFT framework. They develop a planar-coordinate construction where horizon entropy corresponds to mutual information across a boundary sphere, and show that in a dS3/CFT2 setting the mutual entropy scales with the central charge and the UV cutoff set by the de Sitter scale. Through an analytic continuation from AdS to de Sitter, they relate nonunitarity in the dS CFT and field masses to AdS boundary conditions, and interpret static-coordinate entropy as entanglement across energy scales. They argue that unitary time evolution imposes a fundamental entropy bound tied to and that exceeding this bound signals a phase transition or naked singularity in the AdS picture, thereby linking holographic entanglement, RG flow, and cosmological entropy in a unified framework.

Abstract

We propose that the entropy of de Sitter space can be identified with the mutual entropy of a dual conformal field theory. We argue that unitary time evolution in de Sitter space restricts the total number of excited degrees of freedom to be bounded by the de Sitter entropy, and we give a CFT interpretation of this restriction. We also clarify issues arising from the fact that both de Sitter and anti de Sitter have dual descriptions in terms of conformal field theory.

Paper Structure

This paper contains 10 sections, 53 equations, 2 figures.

Table of Contents

  1. Introduction
  2. de Sitter / CFT duality
  3. de Sitter entropy in planar coordinates
  4. Mutual entropy
  5. Mutual entropy in quantum field theory
  6. Mutual entropy in conformal field theory
  7. Mutual entropy and de Sitter entropy
  8. From AdS to de Sitter space
  9. Entropy in static coordinates
  10. Entropy and time evolution

Figures (2)

  • Figure 1: Penrose diagram for de Sitter space. We've indicated the two cosmological horizons as well as a fixed-time hypersurface in the planar coordinate system.
  • Figure 2: The dashed line is a contracting light-sheet, which begins at the south pole and intersects the constant-$\eta$ hypersurface at $x^i x^i = R^2$.