Double-Scaled SYK, QCD, and the Flat Space Limit of de Sitter Space (2501.09423v1)

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.

• The paper establishes a novel correspondence where the large-N expansion in DSSYK mirrors the 't Hooft expansion in QCD through organized genus expansions.
• The study rigorously compares perturbative and non-perturbative calculations, showing emergent string-like behavior analogous to confinement in QCD.
• The analysis suggests a promising duality framework linking holographic descriptions in de Sitter space with insights from SYK and QCD, opening avenues for new computational techniques.

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

The paper explores the intriguing parallels between Double-Scaled Sachdev-Ye-Kitaev (DSSYK) model at infinite temperature and large $N$ Quantum Chromodynamics (QCD). This connection arises from the observation that the large $N$ expansions of DSSYK and QCD share a common structure. Specifically, the 't Hooft limit of QCD is analogous to the fixed $p$ limit of the SYK model with $p$-local interactions, and the fixed gauge coupling in AdS/CFT corresponds to the double-scaled limit of SYK.

Key Numerical Results and Claims

The paper presents a rigorous examination of the perturbative and non-perturbative calculations in DSSYK, comparing these with known properties of Yang-Mills theory. The similarity is demonstrated through the organization of correlation functions in both theories into genus expansions, which in DSSYK manifests in the large $N$ expansion aligning with the 't Hooft expansion in QCD. This reveals a fundamental correspondence where $N$ in SYK relates to $N_c^2$ in QCD.

Furthermore, the implications of these results suggest that the fixed $\lambda$ limit exists for DSSYK, similar to the ultra-strongly coupled regime of QCD at fixed gauge coupling. This non-trivial conclusion implies potential analogs in terms of the confinement dynamics, as observed through the emergent scales regulating infrared divergences, like the string length scale emergence in DSSYK.

Theoretical Implications

The theoretical implications of this paper are significant. The correspondence hints at a deeper understanding of holography in de Sitter space, providing insights into the structure of QFTs in Rindler space. Particularly, the creation of a "phase boundary" akin to a stretched horizon in holographic descriptions of de Sitter space and its relation to confinement in QCD encapsulates the emergence of new scales and dynamics.

For DSSYK, where the emergent string-like behavior parallels confinement in QCD, the medium-term research trajectory could involve identifying a detailed duality framework, addressing the conjectured DSSYK-de Sitter correspondence. Insight into how string-worldsheet-like structures manifest in non-matrix theories like DSSYK could pave the way for novel computational techniques and experimental realizations, further clarifying the roles of both branched polymers and potential non-string constructs in these theories.

Future Developments

Moving forward, expanding the understanding of how primitive diagrams and their decorated forms contribute to the fixed $\lambda$ limit, along with further exploring the implications of branched polymers within DSSYK, emerges as a promising area. The potential for identifying localized string worldsheet features even in theories lacking explicit matrix structures suggests an exciting avenue for theoretical development.

The empirical parallels noted between the fixed $N_c^2$ limit of gauge theories and SYK models could motivate revisiting and refining established frameworks, potentially leading toward a unified formalism within the holographic gauge/gravity duality, incorporating both ads and de Sitter spaces under broader circumstances than previously considered.

In conclusion, the paper makes a compelling case for further research across both SYK models and holographic theories, advancing the quest for a cohesive understanding of quantum field theories, their interrelations, and their emergent phenomena in various spacetime backgrounds.