When do real observers resolve de Sitter's imaginary problem?

Abstract

The universal phase $\rev{\ii}^{D+2}$ of the Euclidean de Sitter path integral obstructs a straightforward state-counting interpretation of the Gibbons--Hawking entropy. Building on Maldacena's proposal that specific black-hole observers can reorganize this phase, we derive a general constraint on when such ``real observers'' can succeed. By distinguishing \emph{gravitational observers} from \emph{topological spectators}, we show that any sector whose \emph{infrared effective} action is metric independent at the de Sitter saddle factorizes in the path integral, $\Ztot = \Zgrav^{(\text{obs})}\Ztop$, so the imaginary phase persists regardless of the sector's information-processing capabilities. Using confining $\SU(3)$ gauge theory and topological orders as examples, we demonstrate that an information-bearing clock is necessary but insufficient: only observers whose fluctuations share the negative modes of the conformal factor belong to the special class that can remove the de Sitter phase.

Figures (1)

• Figure 1: Schematic relation between worldlines, informational clocks, and gravitational observers. The Maldacena mechanism operates only in the triple intersection, where a system both carries a clock and backreacts on the conformal factor so as to share its negative modes. Sectors that have worldlines and clocks but decouple from the metric (bottom overlap) are topological spectators: they can store and order information, but they cannot modify the universal de Sitter phase.