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Explore a conference talk examining the numerical regularization of 3D conformal field theories through the innovative "fuzzy sphere" method, which utilizes non-commutative geometry of the lowest Landau level filled by electrons. Discover how this approach achieves regularization by leveraging the Pauli exclusion principle at filling factor v=1, where charge remains trivially gapped while electron spins encode the desired CFT behavior. Learn about successful applications to paradigmatic CFTs like the 3D Ising model and investigate the critical question of how precisely tuned the underlying electron system must be for effective implementation. Examine groundbreaking findings demonstrating that the 3D Ising CFT can be realized at fractional electron fillings, remaining unaffected by particle exchange statistics or topological order nature in the charge sector. Understand how the CFT spectrum becomes intertwined with the charge-neutral spectrum of fractional quantum Hall states in these cases, creating a complex interaction absent in the previously studied v=1 scenario. Analyze the remarkable suppression of mixing between CFT and FQH spectra within numerically-accessible system sizes, revealing important insights for the practical application of this regularization technique in theoretical physics research.
