Fuzzy Sphere Meets CFT: 3D Ising, Fermions and Gauge Theories

In this series of lectures, I will introduce the « fuzzy (non-commutative) sphere regularization, » a recently proposed non-perturbative approach to 3D CFTs. I will first elucidate its fundamental concepts and then dive into illustrative examples, including the 3D Ising transition, fermionic CFTs, and Chern-Simons matter theories. I will comment on the potential theoretical direction in understanding fuzzy sphere regularization from the aspect of algebra on fuzzy sphere.