Fuzzy Sphere regularization of 3D CFTs

by Yin-Chen He

Tuesday 2 Apr 2024, 15:00 → 16:30 Europe/Zurich

4/3-006 - TH Conference Room (CERN)

Conformal Field Theory (CFT) represents a class of quantum field theories that have 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 dive into illustrative examples, including the 3D Ising transition, conformal defects, and critical gauge theories. Importantly, I will 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.

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