Holography on the Quantum Disk

Motivated by recent observations in double-scaled SYK (DSSYK), this talk will feature work in progress analyzing holography on a non-commutative analogue of the hyperbolic disk known as the quantum disk. I will briefly review hints of non-commutative geometry in the chord description of DSSYK, and point out how it lingers in the continuum limit at finite temperature on the recently studied “fake disk.” I’ll then introduce the quantum disk and derive its non-commutative nature, and analyze the dynamics of fields propagating on the fixed quantum disk background. I will point out some notable features of this system including discreteness of space and UV finiteness. I will also describe the implications of the non-commutativity on properties of its putative boundary dual.