Black holes, quantum chaos, and the Riemann hypothesis
Panagiotis Betzios, Nava Gaddam, Olga Papadoulaki
SciPost Phys. Core 4, 032 (2021) · published 10 December 2021
- doi: 10.21468/SciPostPhysCore.4.4.032
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Abstract
Quantum gravity is expected to gauge all global symmetries of effective theories, in the ultraviolet. Inspired by this expectation, we explore the consequences of gauging CPT as a quantum boundary condition in phase space. We find that it provides for a natural semiclassical regularisation and discretisation of the continuous spectrum of a quantum Hamiltonian related to the Dilation operator. We observe that the said spectrum is in correspondence with the zeros of the Riemann zeta and Dirichlet beta functions. Following ideas of Berry and Keating, this may help the pursuit of the Riemann hypothesis. It strengthens the proposal that this quantum Hamiltonian captures the near horizon dynamics of the scattering matrix of the Schwarzschild black hole, given the rich chaotic spectrum upon discretisation. It also explains why the spectrum appears to be erratic despite the unitarity of the scattering matrix.
Cited by 13
Authors / Affiliations: mappings to Contributors and Organizations
See all Organizations.- 1 Πανεπιστήμιο Κρήτης / University of Crete [UOC]
- 2 Universiteit Utrecht / University of Utrecht [UU]
- 3 Centro Internazionale di Fisica Teorica Abdus Salam / Abdus Salam International Centre for Theoretical Physics [ICTP]