Degenerate chords in double-scaled SYK

TL;DR

This paper explores the special properties of matter operators in double-scaled SYK at a degenerate dimension, revealing recursion relations that simplify the calculation of two-point functions.

Contribution

It introduces a novel approach using null vector equations and fusion properties to compute correlation functions without summing infinite diagrams.

Findings

Operators at dimension -1/2 form degenerate representations.

Recursion relations enable direct calculation of two-point functions.

Simplifies analysis of matter correlations in double-scaled SYK.

Abstract

The matter operator in the double-scaled SYK model exhibits special properties when its dimension is analytically continued to -1/2. At this dimension, the operator is in a degenerate representation of the q-deformed oscillator algebra and satisfies a null vector equation. Its peculiar fusion property gives rise to recursion relations among matter correlation functions. We find that these relations allow us to determine the two-point function without having to sum over infinitely many chord diagrams.