Doubled Hilbert space in double-scaled SYK

TL;DR

This paper presents a new formalism for matter correlators in double-scaled SYK using a doubled Hilbert space, revealing a structure involving entanglers and disentanglers for computing correlators.

Contribution

It introduces a novel doubled Hilbert space approach for matter correlators in DSSYK, with explicit structures for two- and four-point functions.

Findings

Matter correlators expressed in doubled Hilbert space

Operator counting chord intersections involves entanglers and disentanglers

Explicit calculations for two- and four-point functions

Abstract

We consider matter correlators in the double-scaled SYK (DSSYK) model. It turns out that matter correlators have a simple expression in terms of the doubled Hilbert space $\mathcal{H}\otimes\mathcal{H}$, where $\mathcal{H}$ is the Fock space of $q$-deformed oscillator (also known as the chord Hilbert space). In this formalism, we find that the operator which counts the intersection of chords should be conjugated by certain ``entangler'' and ``disentangler''. We explicitly demonstrate this structure for the two- and four-point functions of matter operators in DSSYK.