Comments on a Paper by Narovlansky and Verlinde

TL;DR

This note defends the standard holographic link between horizon area and entropy in de Sitter space within the DSSYK∞ framework, arguing that Narovlansky and Verlinde's conclusions arise from two incorrect assumptions. It clarifies multiple temperature notions (Boltzmann, Hawking/Tomperature, chord temperature) and the impact of unit conventions (cosmic/string/micro) on energy scales, showing the Hawking temperature in string units should be J_0/p rather than J_0. The authors demonstrate that correcting these points restores the expected S_dS ~ N scaling and maintains the boundary entropy–bulk area relation, while explaining why backreaction states lie in the non-Gaussian tails of the spectrum. Overall, the work reinforces de Sitter holography in the double-scaled SYK context and sharpens the interpretation of bulk masses, deficit angles, and spectral locations of backreacting states.

Abstract

The double-scaled infinite temperature limit of the SYK model has been conjectured by Rahman and Susskind (RS) [1, 2, 3, 4], and independently by Verlinde [5] to be dual to a certain low dimensional de Sitter space. In a recent discussion of this conjecture Narovlansky and Verlinde (NV) [6] came to conclusions which radically differ from those of RS. In particular these conclusions disagree by factors which diverge as $N \to \infty$. Among these is a mismatch between the scaling of boundary entropy and bulk horizon area. In this note, we point out differences in two key assumptions made by RS and NV which lead to these mismatches, and explain why we think the RS assumptions are correct. When the NV assumptions, which we believe are unwarranted, are replaced by those of RS, the conclusions match both RS and the standard relation between entropy and area. In the process of discussing these, we will shed some light on: the various notions of temperature that appear in the duality; the relationship between Hamiltonian energy and bulk mass; and the location of bulk conical defect states in the spectrum of DSSYK$_{\infty}$.

Figures (3)

• Figure 1: The various scales that appear in ${\rm DSSYK_{\infty}}$/dS$_3$ plotted logarithmically.
• Figure 2: Schematic picture of deficit angle vs $v$ for increasing $p$.
• Figure 3: Schematic picture for the nonlocal coupling term $\upphi\star\upphi\star\upphi$, where the dots on the right hand side correspond to the positions of the three field insertions.