Aspects of Holographic Duality: Pole-Skipping and Deep Learning

Abstract

This thesis investigates two aspects of holographic duality: the structural phenomenon of pole-skipping in various gravitational models, and the inverse modeling of strange metal transport using deep learning. Pole-skipping, initially illuminated through its connection to quantum chaos via special points in retarded Green’s functions, is examined here more broadly as a structural feature of holographic correlators. We study pole-skipping in (1) Jackiw–Teitelboim (JT) gravity and the SYK model, (2) rotating BTZ black holes, and (3) charged black holes with axion fields. In each case, we identify pole-skipping points using various analytic techniques, including near-horizon analysis. We explore how these points persist or deform under different conditions, such as black hole rotation in the bulk and momentum relaxation in the boundary theory. Our results support the view that pole-skipping encodes structural information about holographic duality, not limited to chaotic regimes. In a separate direction, we address the linear-in-temperature resistivity of strange metals using physics-informed neural networks (PINNs). Within an Einstein–Maxwell–Dilaton–Axion framework, we reconstruct bulk holographic potentials that reproduce the desired boundary transport behavior. This data-driven approach demonstrates the potential of machine learning to explore holographic models consistent with experimental observations. Together, these studies deepen our understanding of holographic response functions and demonstrate how both analytic and computational methods can reveal structural and phenomenological insights into strongly coupled quantum systems.