Is There Really a de Sitter/CFT Duality

TL;DR

The paper argues that de Sitter complementarity precludes the standard dS/CFT boundary correlators in a finite-entropy de Sitter space, contrasting with infinite-entropy QFT where correlations decay. It shows that finite horizon entropy leads to a discrete spectrum and inevitable Poincaré recurrences, producing chaotic late-time fluctuations and a nonzero long-time average, thereby obstructing a conventional local boundary CFT description. Through both analytic arguments and a random-matrix Appendix, the authors illustrate that boundary observables in de Sitter space would require nonstandard, nonlocal constructs or rely on nonperturbative topology-sum effects. These results challenge the viability of a straightforward dS/CFT duality for cosmological horizons and highlight fundamental limits on holographic descriptions of de Sitter space.

Abstract

In this paper a de Sitter Space version of Black Hole Complementarity is formulated which states that an observer in de Sitter Space describes the surrounding space as a sealed finite temperature cavity bounded by a horizon which allows no loss of information. We then discuss the implications of this for the existence of boundary correlators in the hypothesized dS/cft correspondence. We find that dS complementarity precludes the existence of the appropriate limits. We find that the limits exist only in approximations in which the entropy of the de Sitter Space is infinite. The reason that the correlators exist in quantum field theory in the de Sitter Space background is traced to the fact that horizon entropy is infinite in QFT.

Figures (7)

• Figure 1: Large time behavior of correlation functions for (a) N=5, (b) N=10 and (c) N=20
• Figure 2: Correlation recurrences for N=20, showing initial falloff and fluctuations
• Figure 3: Correlation recurrences for N=20: (a) 50%, (b) 70%
• Figure 4: Recurrence time as a function of absolute size of fluctuations
• Figure 5: Recurrence time as a power of $e^S$