The late time ramp from chord diagrams in the double-scaled SYK model

TL;DR

This paper analytically derives the late-time spectral form factor ramp in double-scaled SYK using chord diagrams, connecting random matrix theory and operator basis, and extends the analysis to finite q.

Contribution

It introduces a chord diagram approach to compute the late-time ramp in double-scaled SYK and relates it to topological recursion methods.

Findings

Reproduces the eigenvalue correlations in random matrix theory from chord diagrams.

Identifies operators responsible for the late-time ramp.

Extends the computation to finite q, confirming the expected ramp behavior.

Abstract

We compute the ramp of the spectral form factor analytically from chord diagrams in double scaled SYK. We map the double-trace correlator to a sum of single trace two-point functions over a basis of operators. We then reproduce the local eigenvalue correlations in random matrix theory from the chord diagrams perspective, which is the $q= 0$ limit of double scaled SYK, and identify the relevant operators that give rise to the late-time ramp. We then extend the computation to finite $q$, resulting in the late time contribution to the spectral form factor. We verify that the late time asymptotics of the finite $q$ computation gives rise to the expected late time ramp. Our computation also provides the corresponding trumpet partition function and gluing factor for chords, which form the basis of a chord analog to topological recursion.