“Exact Solutions in Conformal Field Theories via Brownian Loop Soups”
Giovedì 10 Aprile 2025, ore 11:00 12:30 - Sala Riunioni 7B2 Aula 1BC45 - Alberto Gandolfi (NYU - Abu Dhabi)
Abstract
This seminar will explore recent advances in constructing conformal field theories (CFT) from probabilistic objects, focusing on the Brownian Loop Soup. Inspired by conformal invariance and statistical mechanics, we discuss how the Brownian Loop Soup naturally gives rise to conformal correlation functions and scalar conformal primary fields. By means of exact solutions and rigorous probabilistic frameworks, we demonstrate that loop ensembles can explicitly realize models of CFT. Although more elaborate fields have been identified in more recent works by Jego, Lupu and Qian, our approach uniquely allows for explicit, analytically tractable solutions. The presented results, based on joint works with Federico Camia, Matthew Kleban, Valentino Foit, Tulasi Ram Reddy Annapareddy, Giovanni Peccati, and Nina Holden, emphasize how classical stochastic processes yield exact and analytically tractable examples of conformally invariant quantum fields.
Seminars in Probability and Finance
