Where is the Entropy in DSSYK-de Sitter? Correction to a wrong claim

TL;DR

This paper corrects a previous misconception about the location of entropy in DSSYK-de Sitter space, clarifying it resides at a Planck-scale distance from the horizon rather than a string-scale distance.

Contribution

It revises the understanding of entropy localization in DSSYK/de Sitter space by correcting earlier claims based on a misconception about the confinement-deconfinement transition.

Findings

Entropy resides at a Planck distance from the horizon.

The previous claim of string-distance localization was based on a misconception.

The corrected position differs by a factor of rom the earlier estimate.

Abstract

A question arises in the holographic description of the static patch of de Sitter space: Where does the entropy reside? The answer of course is in the stretched horizon, but how far from the mathematical horizon is the stretched horizon? In recent papers and lectures I argued that the entropy in DSSYK/JT-de Sitter resides at a string distance from the horizon. That conclusion was based on misconception about the confinement-deconfinement transition in the 't Hooft model. When corrected the right answer is of order the Planck distance (which differs from the string distance by a factor of order $\sqrt{N}).$