Appears in collection : Fuzzy Sphere Meets Conformal Bootstrap 2025

Gauge theories are not only the IR descriptions of many exotic critical phases and transitions, but also one of the few known methods for constructing interacting CFTs in 3d. Obtaining their conformal data has been a rewarding pursuit. In this talk, I present a construction of critical gauge theories on the fuzzy sphere through an intermediate step of the non-linear σ-model (NLSM) with Wess-Zumino-Witten (WZW) term. I demonstrate how fuzzy sphere models can be matched with NLSM-WZW, and how NLSM-WZW can correspond to critical gauge theories. As a concrete example, I focus on the discovery of a series of Sp(N)-symmetric CFTs corresponding to the NLSM on symplectic Grassmannians, whose most natural candidates are Chern-Simons theories coupled to critical scalar/fermion fields. I present the numerical evidence for emergent conformal symmetry and discuss their operator contents. I will also briefly highlight some of our other progress on the fuzzy sphere, including conformal defects, boundaries and our numerical package FuzzifiED.