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Explore advanced theoretical physics concepts in this Institute for Advanced Study High Energy Theory Seminar lecture examining three-dimensional conformal field theories through the innovative lens of the fuzzy sphere framework. Delve into the critical role of 3D CFTs in both condensed-matter and high-energy physics, with particular emphasis on critical gauge theories and Chern-Simons-matter theories that describe topologically ordered phase transitions and host conjectured dualities with potential experimental realization in Moiré materials. Discover how the fuzzy sphere provides exceptional computational efficiency while bridging CFTs with quantum Hall physics through detailed analysis of the confinement transition of the ν=1/2 bosonic Laughlin state described by a scalar coupled to a U(1)_2 gauge field. Learn about the continuous nature of this transition with emergent conformal symmetry and examine its critical properties. Investigate groundbreaking realizations of free and interacting fermionic CFTs, including the free Majorana fermion and super-Ising theory, implemented through boson-fermion mixture setups. Gain insights into future research directions encompassing QED with Chern-Simons, broader Lagrangian quantum field theories, and super-conformal field theories, presented by Zheng Zhou from the Perimeter Institute.
