Solving Conformal Defects in 3D Conformal Field Theory using Fuzzy Sphere Regularization

Abstract

Defects in conformal field theory (CFT) are of significant theoretical and experimental importance. The presence of defects theoretically enriches the structure of the CFT, but at the same time, it makes it more challenging to study, especially in dimensions higher than two. Here, we demonstrate that the recently-developed theoretical scheme, \textit{fuzzy (non-commutative) sphere regularization}, provides a powerful lens through which one can dissect the defect of 3D CFTs in a transparent way. As a notable example, we study the magnetic line defect of 3D Ising CFT and clearly demonstrate that it flows to a conformal defect fixed point. We have identified 6 low-lying defect primary operators, including the displacement operator, and accurately extract their scaling dimensions through the state-operator correspondence. Moreover, we also compute one-point bulk correlators and two-point bulk-defect correlators, which show great agreement with predictions of defect conformal symmetry, and from which we extract various bulk-defect operator product expansion coefficients. Our work demonstrates that the fuzzy sphere offers a powerful tool for exploring the rich physics in 3D defect CFTs.

An error in $C_D$ in previous version has been corrected. 15 pages, 9 figures

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• The $g$-function and Defect Changing Operators from Wavefunction Overlap on a Fuzzy Sphere
• Studying the 3d Ising surface CFTs on the fuzzy sphere
• Constructing the Infrared Conformal Generators on the Fuzzy Sphere
• Exact Diagonalization, Matrix Product States and Conformal Perturbation Theory Study of a 3D Ising Fuzzy Sphere Model
• Regularizing 3D conformal field theories via anyons on the fuzzy sphere
• Easy bootstrap for the 3D Ising model: a hybrid approach of the lightcone bootstrap and error minimization methods
• Defect conformal field theory from Sachdev-Ye-Kitaev interactions
• Numerical extraction of crosscap coefficients in microscopic models for (2+1)D conformal field theory
• Probing Defects with Quantum Simulator Snapshots
• From Weyl Anomaly to Defect Supersymmetric Rényi Entropy and Casimir Energy