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De Sitter Space has no Chords. Almost Everything is Confined

Leonard Susskind

TL;DR

This paper proposes that the double-scaled, infinite-temperature SYK model (DSSYK_infty) holographically describes de Sitter space, with a confinement mechanism essential to preventing an unphysical proliferation of bulk degrees of freedom. By analyzing both the gravity side (JT de Sitter, emergent string scale, and sub-dS locality) and the DSSYK_infty model (real and complex fermions, large-N perturbation theory, and chord/cord dynamics), the author argues that almost all boundary fermionic degrees are confined to the stretched horizon, leaving only SU(N) singlets to propagate into the bulk. Key results include the identification of an emergent string scale M_s = J q, L_s = 1/(J q), the demonstration that non-singlet states acquire imaginary energies and are confined, and the QCD-plasma analogy that clarifies the bulk-bath separation. The findings offer a mechanism to reconcile de Sitter holography with bulk locality and provide a concrete framework for sub-dS locality in a holographic de Sitter model, with implications for understanding Hawking radiation and horizon dynamics.

Abstract

This paper describes a phenomenon in which all but a tiny fraction of the fundamental holographic degrees of the SYK theory are confined (as in quark confinement) in the double-scaled infinite temperature limit. The mechanism for confinement is an essential ingredient in the duality between DSSYK and de Sitter space. The mechanism, which removes almost all states from the physical spectrum of the bulk de Sitter theory applies to configurations of a small number of fermions which would be expected to comprise Hawking radiation in de Sitter space. Without confinement there would be far too many species of Hawking particles. The mechanism also applies to configurations with larger number of fermions, including the objects described by chord diagrams.

De Sitter Space has no Chords. Almost Everything is Confined

TL;DR

This paper proposes that the double-scaled, infinite-temperature SYK model (DSSYK_infty) holographically describes de Sitter space, with a confinement mechanism essential to preventing an unphysical proliferation of bulk degrees of freedom. By analyzing both the gravity side (JT de Sitter, emergent string scale, and sub-dS locality) and the DSSYK_infty model (real and complex fermions, large-N perturbation theory, and chord/cord dynamics), the author argues that almost all boundary fermionic degrees are confined to the stretched horizon, leaving only SU(N) singlets to propagate into the bulk. Key results include the identification of an emergent string scale M_s = J q, L_s = 1/(J q), the demonstration that non-singlet states acquire imaginary energies and are confined, and the QCD-plasma analogy that clarifies the bulk-bath separation. The findings offer a mechanism to reconcile de Sitter holography with bulk locality and provide a concrete framework for sub-dS locality in a holographic de Sitter model, with implications for understanding Hawking radiation and horizon dynamics.

Abstract

This paper describes a phenomenon in which all but a tiny fraction of the fundamental holographic degrees of the SYK theory are confined (as in quark confinement) in the double-scaled infinite temperature limit. The mechanism for confinement is an essential ingredient in the duality between DSSYK and de Sitter space. The mechanism, which removes almost all states from the physical spectrum of the bulk de Sitter theory applies to configurations of a small number of fermions which would be expected to comprise Hawking radiation in de Sitter space. Without confinement there would be far too many species of Hawking particles. The mechanism also applies to configurations with larger number of fermions, including the objects described by chord diagrams.
Paper Structure (29 sections, 80 equations, 16 figures)

This paper contains 29 sections, 80 equations, 16 figures.

Table of Contents

  1. Introduction
  2. De Sitter Space has no Chords
  3. Almost Everthing is Confined
  4. Gravity Side of the Duality
  5. JT from 3-D De Sitter
  6. Mass and Length Scales in dS
  7. The Case of 4 Dimensions
  8. 3-D
  9. String Scale
  10. The Separation of Scales
  11. Hawking Radiation
  12. DSSYK$_{\bf {\infty}}$
  13. The Hamiltonian
  14. Complex SYK
  15. Dictionary
  16. ...and 14 more sections

Figures (16)

  • Figure 1: Chords are represented by $X$. The number of chords is proportional to the length of the throat.
  • Figure 2: Mass scales in 4 dimensional dS. The horizontal axis represents $\log{M}.$ Mass scales increase to the right and length scales decrease.
  • Figure 3: Mass scales in 3 dimensional including the string scale. Typically the string mass scale will lie near but somewhat below the geometric mean of $M_{min}$ and $M_{max}.$
  • Figure 4: A mass close to the Planck mass in 3-dimensional de Sitter space creates a conical deficit close to $2\pi.$ The geometry is a thin sliver with the edges identified.
  • Figure 5: A vertex for the case $q=6.$
  • ...and 11 more figures