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, the 3D Ising transition, conformal defects and gauge theories. 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.