Lee-Yang on the Fuzzy Sphere - Introduction

Explore the Lee-Yang theorem and its application to conformal field theory through a comprehensive mathematical physics lecture that examines the 3D Lee-Yang CFT using a Fuzzy Sphere regulator. Begin with a thorough review of the Lee-Yang theorem and the associated Lee-Yang conformal field theory, then delve into the construction of a novel model that deforms the Ising model on the Fuzzy Sphere with a purely imaginary longitudinal magnetic field to induce a quantum phase transition. Discover 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 states of the Hamiltonian correspond remarkably well with the expected CFT spectrum. Examine Fuzzy Sphere estimates for the scaling dimension ∆ϕ of the lowest primary operator and understand how small deviations from expected CFT values can be interpreted through leading irrelevant operators. Conclude by analyzing how the Fuzzy Sphere results demonstrate consistency with the most accurate available five-loop ϵ-expansion estimates, providing valuable insights into the intersection of statistical mechanics, quantum field theory, and mathematical physics.