Fuzzy sphere regularization of 3D CFTs

Conformal Field Theory (CFT) represents a class of quantum field theories that has profound applications across various physics domains, from critical phenomena in statistical mechanics to quantum matter, quantum gravity, and string theory. In this talk, I will introduce our recently proposed 'fuzzy (non-commutative) sphere regularization' scheme, a method that addresses and offers a solution to the longstanding need for a non-perturbative approach to 3D CFTs. I will first elucidate its fundamental concepts and then diving into illustrative examples, particularly, the 3D Ising transition. Specifically, we showcase that this scheme is not only potent—revealing a wealth of universal data on 3D CFTs otherwise inaccessible through existing methods—but also efficient, as the necessary computations can be performed on a laptop within an hour. Our innovative scheme not only heralds a new era for the study of CFTs but also hints at a profound interplay between non-commutative geometry and both CFTs and QFTs at large.