Double-Scaled SYK, QCD, and the Flat Space Limit of de Sitter Space

TL;DR

This paper explores the connection between double-scaled SYK, large N QCD, and the flat space limit of de Sitter space, providing insights into gauge theories and holography through perturbative and non-perturbative analyses.

Contribution

It establishes a novel correspondence between double-scaled SYK and large N QCD in the flat space limit, offering a new perspective on gauge theories and holography.

Findings

Demonstrates the parallel between SYK and QCD large N expansions.

Provides perturbative and non-perturbative calculations of DSSYK.

Suggests implications for the de Sitter space holographic duality.

Abstract

A surprising connection exists between double-scaled SYK at infinite temperature, and large N QCD. The large N expansions of the two theories have the same form; the 't Hooft limit of QCD parallels the fixed p limit of SYK (for a theory with p-fermion interactions), and the limit of fixed gauge coupling g -- the flat space limit in AdS/CFT -- parallels the double-scaled limit of SYK. From the holographic perspective fixed g is the far more interesting limit of gauge theory, but very little is known about it. DSSYK allows us to explore it in a more tractable example. The connection is illustrated by perturbative and non-perturbative DSSYK calculations, and comparing the results with known properties of Yang Mills theory. The correspondence is largely independent of the conjectured duality between DSSYK and de Sitter space, but may have a good deal to tell us about it.