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arXiv · 2505.07655

Flowing from the Ising Model on the Fuzzy Sphere to the 3D Lee-Yang CFT

Joan Elias Miro·Olivier Delouche
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Abstract

We employ the Fuzzy Sphere regulator to study the 3D Lee-Yang CFT. The model is defined by deforming the Ising model on the Fuzzy Sphere via a purely imaginary longitudinal magnetic field. This model undergoes a quantum phase transition, whose critical point we determine and identify with the 3D Lee-Yang CFT. We show how to tune the model and find that the lowest-lying states of the Hamiltonian align well with the expected CFT spectrum. We discuss the Fuzzy Sphere estimates for the scaling dimension $Δ_ϕ$ of the lowest primary operator. Finally, we interpret small deviations from the CFT expectations in terms of the leading irrelevant operators of the Lee-Yang CFT. We show that the Fuzzy Sphere calculations are compatible with the best five-loop $ε$-expansion estimates.

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Joan Elias Miro, Olivier Delouche. 2025-05-29. Flowing from the Ising Model on the Fuzzy Sphere to the 3D Lee-Yang CFT. https://arxiv.org/abs/2505.07655

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