Bootstrapping confinement and black hole phase transitions with AI

• Applicant: Dr. Julien Barrat
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: since 2026
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 570367913

Quarks, the fundamental constituents of protons and neutrons, are bound by the strong force, a phenomenon known as confinement. At high temperatures, such as in the early Universe, quarks transition into a deconfined state, which has been observed in particle accelerators. This phase transition occurs in a regime that is difficult to access with traditional tools, necessitating new non-perturbative approaches. In a vastly different physical context, black holes also probe early-Universe conditions where quantum and gravitational effects are strong. They undergo a phase transition through evaporation, raising fundamental questions about information loss in gravity. A theoretical framework to describe this transition is lacking and requires new tools suited for strongly-coupled gravitational systems. These seemingly unrelated problems are connected through holography, in which black holes are equivalent to confining gauge theories in one dimension less. While current holographic correspondences do not directly describe our Universe, they provide a powerful framework for investigating the phase transitions of quarks and black holes within a unified setting. In this context, the relevant gauge theories are conformal field theories (CFTs) at finite temperature and volume. The conformal bootstrap has been highly successful in studying infinite-volume, zero-temperature CFTs non-perturbatively, but this regime does not exhibit phase transitions. This proposal aims to develop new bootstrap methods for CFTs at finite temperature and volume. I will construct a framework that exploits the fact that these theories preserve local properties of the conformal symmetry, while incorporating global periodicity constraints. Using analytic and numerical methods, I will study how these constraints relate to phase transitions. I will implement reinforcement learning algorithms to optimize numerical estimations and efficiently navigate the solution space. This research builds on my expertise in CFTs with broken conformal symmetry, specifically finite-temperature CFTs and conformal defects. Defects serve as valuable probes of a system’s phase—Wilson loops, for example, detect the confinement-deconfinement transition. The research will be conducted at Princeton University and the University of Hamburg, institutions ideally suited for this project. This is the first study to apply bootstrap methods to finite-volume CFTs while integrating machine learning to enhance predictive accuracy. It aims to break substantial new ground in the study of phase transitions in conformal systems. These methods are universal and not limited to holographic theories: They can also be used to study experimentally relevant condensed-matter systems. The application of machine learning to bootstrap techniques has the potential to deliver precise quantitative insights into strongly-coupled quantum field theories, providing new theoretical tools for the study of non-perturbative phenomena.

• DFG Programme: WBP Fellowship
• International Connection: USA
• Host: Professor Dr. Simone Giombi