Where is the Entropy in DSSYK-de Sitter? Correction to a wrong claim
Leonard Susskind
TL;DR
The paper addresses where entropy resides in the holographic description of the de Sitter static patch, correcting a prior claim that it sits at a string-distance from the horizon. It clarifies notational conventions by identifying $\lambda = g_{open}^2$ and lays out the scale relations among $M_{min}$, $M_{micro}$, $M_{Planck}$, and $M_{string}$, highlighting the open-string nature of the ${\rm tHooft}$ model. The main result is that the stretched horizon is located at a Planck-scale distance, with the confinement-deconfinement transition at $T_c = \Lambda \sqrt{N}$ leading to $\rho_{sh} = T_c^{-1} = g_{open}^{-1} \ell_{planck}$ and $T_c = g_{open} M_{planck}$; this aligns with Planck-scale physics rather than string-scale intuition. A comparison with higher-dimensional string theory shows that, while closed-string theories exhibit a Hagedorn transition at $T_c = M_{string}$, the open-string-only setting yields the Planck-scale horizon entropy, reinforcing the central role of Planck-scale phenomena in the DSSYK/JT-de Sitter holographic correspondence.
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 $\sqrt{N}).$