3D Conformal Field Theories with Sp(N) Global Symmetry on a Fuzzy Sphere

The quest to discover new 3D CFTs has been intriguing for physicists. For this purpose, fuzzy sphere regularization that studies interacting quantum systems defined on the lowest Landau level on a sphere has emerged as a powerful tool. In this Letter, we discover a series of new CFTs with global symmetry Sp(N) in the fuzzy sphere models that are closely related to the SO(5) deconfined phase transition, and are related to a Sp(N)/[Sp(M)×Sp(N-M)] nonlinear sigma model with a Wess-Zumino-Witten term. We numerically verify the emergent conformal symmetry by observing the integer-spaced conformal multiplets, the quality of conformal generators, 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 flavors of gapless bosons or fermions coupled to a non-Abelian [viz. Sp(1), Sp(2), etc.] Chern-Simons gauge field. Our Letter provides new avenues for studying interacting CFTs in 3D, possibly facilitating the nonperturbative study of critical gauge theories and previously undiscovered CFTs.