Doubled Hilbert space in double-scaled SYK

Kazumi Okuyama

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arXiv · 2401.07403

Doubled Hilbert space in double-scaled SYK

Kazumi Okuyama

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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.

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Kazumi Okuyama. 2024-01-15. Doubled Hilbert space in double-scaled SYK. https://arxiv.org/abs/2401.07403

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