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Explore the Lee-Yang theorem and its associated conformal field theory through a comprehensive 30-minute conference talk that introduces a novel Fuzzy Sphere regulator approach to studying the 3D Lee-Yang CFT. Begin with a thorough review of the foundational Lee-Yang theorem and conformal field theory concepts before delving into the construction of a deformed Ising model on the Fuzzy Sphere using a purely imaginary longitudinal magnetic field to induce quantum phase transitions. Examine the main findings from recent research (arXiv:2505.07655) that identifies the critical point of this model with the 3D Lee-Yang CFT, learning how to properly tune the model parameters and observe how the lowest-lying Hamiltonian states correspond remarkably well with expected CFT spectrum predictions. Analyze Fuzzy Sphere estimates for the scaling dimension ∆ϕ of the lowest primary operator, understand the interpretation of small deviations from expected CFT values through leading irrelevant operators, and discover how these Fuzzy Sphere results align consistently with the most accurate five-loop ϵ-expansion estimates available in the field.
