Operator Product Expansion Coefficients of the 3D Ising Criticality via Quantum Fuzzy Sphere

Abstract

Conformal field theory (CFT) is the key to various critical phenomena. So far, most of studies focus on the critical exponents of various universalities, corresponding to conformal dimensions of CFT primary fields. However, other important yet intricate data such as the operator product expansion (OPE) coefficients governing the fusion of two primary fields, is largely unexplored before, specifically in dimensions higher than 2D (or equivalently $1+1$D). Here, motivated by the recently-proposed fuzzy sphere regularization, we investigate the operator content of 3D Ising criticality starting from a microscopic description. We first outline the procedure of extracting OPE coefficients on the fuzzy sphere, and then compute 13 OPE coefficients of low-lying CFT primary fields. The obtained results are in agreement with the numerical conformal bootstrap data of 3D Ising CFT within a high accuracy. In addition, we also manage to obtain 4 OPE coefficients including $f_{T_{\mu \nu }{T}_{\rho \eta }\epsilon }$ that were not available before, which demonstrates the superior capabilities of our scheme. By expanding the horizon of the fuzzy sphere regularization from the state perspective to the operator perspective, we expect a lot of new physics ready for exploration.

12 pages, 3 figures

References in corpus (8)

• The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT
• Density Matrix Renormalization Group Study of Incompressible Fractional Quantum Hall States
• Conformal field theories at non-zero temperature: operator product expansions, Monte Carlo, and holography
• Uncovering conformal symmetry in the $3D$ Ising transition: State-operator correspondence from a fuzzy sphere regularization
• Numerical determination of OPE coefficients in the 3D Ising model from off-critical correlators
• Operator fusion from wavefunction overlaps: Universal finite-size corrections and application to Haagerup model
• Two- and three-point functions at criticality: Monte Carlo simulations of the improved three-dimensional Blume-Capel model
• Two- and three-point functions at criticality: Monte Carlo simulations of the three-dimensional $(q+1)$-state clock model

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