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 \( {U}_q\left(\mathfrak{s}{\mathfrak{u}}_{1,1}\right) \). We review how this algebra is defined and its associated group SUq(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.
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Acknowledgments
We thank Micha Berkooz, Mikhail Isachenkov, Henry Lin, Simon Lin, Ohad Mamroud, Alexei Milekhin and Yifan Wang for insightful discussion and correspondence. F.K.P. is currently a Simons Junior Fellow at New York University and supported by a grant 855325FP from the Simons Foundation.
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Almheiri, A., Popov, F.K. Holography on the quantum disk. J. High Energ. Phys. 2024, 70 (2024). https://doi.org/10.1007/JHEP06(2024)070
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DOI: https://doi.org/10.1007/JHEP06(2024)070