Gravitational Duals from Equations of State II: Large Hierarchies and False Vacua

2026-06-29

AI Summary

This work addresses the challenge of reconstructing the bulk scalar potential in holographic duals of strongly coupled quantum field theories characterized by large hierarchies of energy scales and metastable (false vacuum) structures, a task notoriously difficult from boundary thermodynamic data alone. The authors propose an inversion framework based on physics-informed neural networks (PINNs), integrating holographic duality principles with thermodynamic inversion algorithms and incorporating numerical stability enhancements. This approach effectively overcomes obstacles posed by near-degenerate states, extreme scale separation, and regions lacking empirical data. For the first time, it enables high-precision reconstruction of the scalar potential deep within the false vacuum regime, successfully reproducing the underlying nontrivial thermodynamics and discontinuous renormalization group flows even under pronounced numerical stiffness, thereby extending the frontier of machine learning applications in holographic studies of strongly coupled systems.

Abstract

We investigate the reconstruction of holographic duals for strongly coupled quantum field theories in regimes characterized by large hierarchies and the presence of false vacua. Within the gauge/gravity duality, these features translate into non-trivial thermodynamic behaviour and exotic renormalization group flows, including skipping flows between non-adjacent fixed points. Building on previous work based on Physics-Informed Neural Networks (PINNs), we extend the holographic inverse problem of reconstructing the bulk scalar potential from boundary thermodynamic data into this new regime. This setting presents a variety of conceptual and numerical challenges, such as near-degenerate states, large hierarchies of energy scales, and regions of the potential that are not directly probed by the input data. We develop a set of methodological advances that overcome these obstacles, thereby improving the established PINNs-based methodology and extending it to new physical regimes of interest that were previously out of reach. Applying the developed framework, we demonstrate accurate reconstruction of scalar potentials deep into the false vacuum regime, achieving robust agreement with the physical features of the underlying thermodynamics despite significant numerical stiffness. Our results extend the bridge between holography and machine learning, and suggest that data-driven approaches can provide new insights into the structure of strongly coupled systems.

Problem

• holographic duals
• false vacua
• large hierarchies
• equations of state
• strongly coupled quantum field theories

Innovation

• Physics-Informed Neural Networks
• holographic reconstruction
• false vacua
• large hierarchies
• renormalization group flows