Multi-trace Correlators in the SYK Model and Non-geometric Wormholes

TL;DR

This paper investigates multi-trace correlations in the SYK model, revealing dominant non-geometric fluctuations that surpass topological wormhole contributions, and proposes their implications for dual gravity theories.

Contribution

It introduces a diagrammatic approach to analyze global fluctuations in the SYK model and identifies dominant non-topological correlations that challenge existing wormhole-based interpretations.

Findings

Connected moments are larger than RMT correlations.

Dominant diagrams are 1PI cactus graphs.

New correlations suggest non-geometric bulk fields.

Abstract

We consider multi-energy level distributions in the SYK model, and in particular, the role of global fluctuations in the density of states of the SYK model. The connected contributions to the moments of the density of states go to zero as $N \to \infty$, however, they are much larger than the standard RMT correlations. We provide a diagrammatic description of the leading behavior of these connected moments, showing that the dominant diagrams are given by 1PI cactus graphs, and derive a vector model of the couplings which reproduces these results. We generalize these results to the first subleading corrections, and to fluctuations of correlation functions. In either case, the new set of correlations between traces (i.e. between boundaries) are not associated with, and are much larger than, the ones given by topological wormholes. The connected contributions that we discuss are the beginning of an infinite series of terms, associated with more and more information about the ensemble of couplings, which hints towards the dual of a single realization. In particular, we suggest that incorporating them in the gravity description requires the introduction of new, lighter and lighter, fields in the bulk with fluctuating boundary couplings.