Holography on the Quantum Disk

Abstract

Motivated by recent study of DSSYK and the non-commutative nature of its bulk dual, we review and analyze an example of a non-commutative spacetime known as the quantum disk proposed by L. Vaksman. The quantum disk is defined as the space whose isometries are generated by the quantum algebra $U_q({\mathfrak{su}}_{1,1})$. We review how this algebra is defined and its associated group $S{U}_q(1,1)$ that it generates, highlighting its non-trivial coproduct that sources bulk non-commutativity. We analyze the structure of holography on the quantum disk and study the imprint of non-commutativity on the putative boundary dual.

39 pages; v2: minor modifications to the paper summary in the introduction; v3: JHEP version; v4: minor modifications