Factorizing Wormholes in a Partially Disorder-Averaged SYK Model

TL;DR

This paper introduces a partially disorder-averaged SYK model with a new set of local collective fields, revealing how half-wormhole saddles emerge as couplings are fixed, bridging fixed and averaged SYK models.

Contribution

It develops a large N effective description with local collective fields that interpolate between disorder-averaged and fixed-coupling SYK models, elucidating the emergence of half-wormholes.

Findings

Local collective fields vanish in the disorder-averaged limit

Nontrivial profiles of local fields develop with fixed couplings

Bulk interpretation links local fields to spacetime branes

Abstract

In this paper, we introduce a "partially disorder-averaged" SYK model. This model has a real parameter that smoothly interpolates between the ordinary totally disorder-averaged SYK model and the totally fixed-coupling model. For the large $N$ effective description, in addition to the usual bi-local collective fields, we also introduce a new additional set of local collective fields. These local fields can be understood as "half" of the bi-local collective fields, and in the totally fixed-coupling limit, they represent the "half-wormholes" which were found in recent studies. We find that the large $N$ saddles of these local fields vanish in the total-disorder-averaged limit, while they develop nontrivial profiles as we gradually fix the coupling constants. We argue that the bulk picture of these local collective fields represents a correlation between a spacetime brane and the asymptotic AdS boundary. This illuminates how the half-wormhole saddles emerge in the SYK model with fixed couplings.