Applied Holography: Holographic Inverse Problems with Machine Learning and Black Hole Quantum Chaos

Abstract

This thesis explores two directions of applied holography within the framework of AdS/CFT. The first direction concerns machine-learning approaches to holographic inverse problems, while the second focuses on the analysis of quantum-chaotic properties of AdS black holes using the brickwall model. We clarify the structure of machine-learning-based holographic inverse problems by con- structing a simple classical mechanics toy model that captures their essential features. The toy model serves as an analogue of holographic inverse problems, in which bulk geometries are reconstructed from boundary data such as the equation of state in QCD and linear-T resistivity in condensed matter systems, and is implemented using the same machine-learning methods. To address a more realistic holographic inverse problem, we take the time-dependent entanglement entropy of AdS black holes—specifically the Page curve associated with the black-hole informa- tion paradox—as input data and use machine learning to infer bulk geometries that reproduce the given entanglement evolution. We find that multiple distinct bulk geometries can gener- ate essentially identical Page curves, demonstrating the non-uniqueness of the correspondence between the Page curve and the underlying black-hole geometry. The second direction investigates the quantum-chaotic properties of hyperbolic AdS black holes by applying the brickwall model with fuzzball-inspired boundary conditions and comput- ing the normal-mode spectrum of a probe scalar field. Building on earlier results for the d = 2 BTZ black hole, we extend the analysis to general (d+1)-dimensional AdS black holes and exam- ine random-matrix-theory diagnostics—including level-spacing statistics, spectral form factors, and Krylov complexity. We show that while random-matrix-type chaotic universality persists at finite dimensions, it is suppressed in the d→∞ limit due to strong spectral degeneracies. This study extends the scope of numerical and applied approaches to holographic corre- spondence by clarifying the structure and applications of inverse holographic problems, and by providing a structural analysis of quantum chaos in black hole spectra.