[Seminar] [HEX-HET] Quantum Symmetry and Geometry from Chords in DSSYK

Jiuci Xu, UCSB

Title: Quantum Symmetry and Geometry from Chords in DSSYK

Abstract: It is well known that the low-energy continuum limit of double-scaled SYK (DSSYK) reduces to JT gravity with matter on the Euclidean disk, where the chord symmetry algebra reduces to a symmetry algebra acting on the disk. It's natural to ask if there is an analogous quantum symmetry and bulk geometric interpretation intrinsic to DSSYK itself, without passing to the continuum?

In this talk, I will explore a quantum symmetry algebra generated by chord operators acting on entangled states in the chord Hilbert space. I will show how the one-particle sector of the chord Hilbert space furnishes (copies of) positive discrete series representation of the quantum group Uq(su(1,1)).  Building on this, we construct multi-particle states in DSSYK through fusion rules of the representation. In particular, the quantum 6j-symbols previously found to be associated with bulk crossing matter chords emerge naturally from the fusion rules of the quantum group.  I will also comment on how these algebraic structures suggest a potential framework for defining a quantum disk with discretized bulk radial direction, and how a discrete notion of horizon might be probed from a boundary algebra.