Integrability, conformal field theory and correlation functions

Gauge theories—the mathematical frameworks describing the fundamental forces of nature—become impossible to solve with standard equations when pushed beyond the simplest cases. This project uses a mathematical technique called integrability to crack those otherwise impenetrable problems, allowing researchers to calculate exact results for quantum field theories that normally resist all attempts at solution. Why this matters: Quantum field theories underpin our understanding of particle physics, from the behaviour of quarks inside protons to the interactions that governed the early universe. Without exact solutions, physicists rely on approximations that break down in many important regimes—for example, when particles interact strongly. Integrability offers a back door, providing precise answers where none existed before. This is fundamental science with no immediate practical application. The payoff is conceptual: a deeper, more complete understanding of how quantum fields behave. Historically, similar advances in mathematical physics—from group theory to gauge-gravity duality—have later found unexpected uses in materials science, quantum computing, and even pure mathematics. A clearer picture of quantum field theories could eventually inform new ways to model complex systems, but that remains decades away. For now, the value lies in knowing what the equations actually say.