Degenerate chords 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.