Cristian Voinea (School of Physics and Astronomy, University of Leeds) – Regularizing 3D conformal field theories via the fuzzy sphere

Understanding the universal properties of continuous phase transitions has been a long-standing area of focus. A powerful tool in this endeavor have been conformal field theories (CFTs) — a class of interacting field theories with a rich symmetry structure that can emerge in statistical mechanics models tuned to a critical point. The recently introduced “fuzzy sphere” method has enabled accurate numerical regularizations of certain three-dimensional (3D) CFTs. The regularization is provided by the non-commutative geometry of the lowest Landau level filled by electrons, such that the charge sector is trivially gapped due to the Pauli exclusion principle at filling factor ν = 1, while the electron spins encode the desired CFT. In this talk, along with key concepts for CFT in 3D, I will provide an overview of the fuzzy sphere method and its application to the paradigmatic 3D Ising CFT. I will also present recent results for encoding the same CFT using strongly correlated fractional quantum Hall states, setting the stage for the fuzzy-sphere exploration of conformal critical points between topologically ordered states.