DSSYK at Infinite Temperature: The Flat-Space Limit and the 't Hooft Model

TL;DR

This work investigates how to extract the bulk flat-space theory from a holographic description of the static patch in de Sitter space, focusing on ${\rm DSSYK_{\infty}}$ at infinite temperature. By exploiting exact and ensemble symmetries, especially the emergent $SU(N)$ in the averaged theory and perfect self-averaging in the double-scaled limit, the authors argue that the bulk dual is the strongly coupled one-flavor $QCD_2$ ('t Hooft model) in $(1+1)$ dimensions, with the boundary open-string parameter $\lambda$ identified as the square of the open string coupling $g_{st}$ via $\lambda = g_{st}^2$. The analysis connects the boundary fermions to bulk quarks, explains confinement mechanisms both to the stretched horizon and within the bulk, and relates a meson Regge tower to a putative DSSYK singlet tower, while embedding the story in the Rindler-space formulation of the static patch. The results offer a concrete realization of de Sitter holography with sub-cosmic locality, where bulk dynamics are governed by a strongly coupled gauge theory rather than weakly coupled gravitons, and highlight the role of symmetry and self-averaging in decoding holographic duals.

Abstract

In the limit of infinite radius de Sitter space becomes locally flat and the static patch tends to Rindler space. A holographic description of the static patch must result in a holographic description of some flat space theory, expressed in Rindler coordinates. Given such a holographic theory how does one decode the hologram and determine the bulk flat space theory, its particle spectrum, forces, and bulk quantum fields? In this paper we will answer this question for a particular case: DSSYK at infinite temperature and show that the bulk theory is a strongly coupled version of the 't Hooft model, i.e., (1+1)-dimensional QCD, with a single quark flavor. It may also be thought of as an open string theory with mesons lying on a single Regge trajectory.

Figures (9)

• Figure 1: Fermion and $JJ$ propagators.
• Figure 2: A diagnotic operator $W$ that depends on the fermion operators (black lines
• Figure 3: The expectation value of $W$ is computed by contracting the fermions but leaving the $JJ$ insertions uncontracted.
• Figure 4: The final step in computing the average of the expectation value of $W$ is to contract the $JJ$ insertions.
• Figure 5: The expectation value of $WW$.