Part IV: Non-Perturbative CFT Bootstrap & Higher-Dimensional Generalizations

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.