A new series of 3D CFTs with $\mathrm{S}\mathrm{p}(N)$ global symmetry on fuzzy sphere

The quest to discover new 3D CFTs has been intriguing for physicists. For this purpose, fuzzy sphere reguarlisation that studies interacting quantum systems defined on the lowest Landau level on a sphere has emerged as a powerful tool. In this paper, we discover a series of new CFTs with global symmetry $\mathrm{S}\mathrm{p}(N)$ in the fuzzy sphere models that are closely related to the $\mathrm{S}\mathrm{O}(5)$ deconfined phase transition, and are described by a $\mathrm{S}\mathrm{p}(N)\mathrm{/}(\mathrm{S}\mathrm{p}(M)\times \mathrm{S}\mathrm{p}(N-M))$ non-linear sigma model with a Wess-Zumino-Witten term. We numerically verify the emergent conformal symmetry by observing the integer-spaced conformal multiplets and studying the finite-size scaling of the conformality. We discuss possible candidates for these newly discovered CFTs, the most plausible ones being Chern-Simons-matter theories which have $N$ flavour of gapless bosons or fermions coupled to a non-Abelian (viz. $\mathrm{S}\mathrm{p}(1)$, $\mathrm{S}\mathrm{p}(2)$, etc.) Chern-Simons gauge field. Our work provides new avenues for studying interacting CFTs in 3D, possibly facilitating the non-perturbative study of critical gauge theories and previously undiscovered CFTs.