Comments on a Paper by Narovlansky and Verlinde

TL;DR

This paper critiques recent differing conclusions on the duality between the double-scaled SYK model at infinite temperature and de Sitter space, defending the original assumptions and clarifying key conceptual issues.

Contribution

It clarifies the assumptions behind the SYK-de Sitter duality and defends the original framework against recent conflicting claims.

Findings

The RS assumptions are more consistent with the entropy-area relation.

Differences in assumptions lead to divergent conclusions about the duality.

Clarifies the notions of temperature and bulk spectrum in the duality.

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$_{\infty}$.