Studying 3D O(N) Surface CFT on the Fuzzy Sphere

TL;DR

This paper applies fuzzy-sphere BCFT methods to study boundary critical phenomena in 2+1D O(N) models, extracting operator spectra, OPE data, and boundary central charges, with results matching Monte Carlo benchmarks.

Contribution

It extends fuzzy-sphere BCFT spectroscopy to continuous O(N) universality classes, providing detailed boundary data and evidence for extraordinary-log criticality.

Findings

Boundary operator spectra and OPE data obtained for O(2) and O(3) models.

Universal amplitudes match Monte Carlo benchmarks where available.

Evidence for positive extraordinary-log exponents in both models.

Abstract

Boundary conformal field theory (BCFT) provides a universal framework for critical phenomena in the presence of boundaries. We determine BCFT data for the normal and ordinary boundary universality classes of the $1+1$-dimensional boundaries of the $2+1$-dimensional $O(2)$ and $O(3)$ Wilson-Fisher fixed points, realized microscopically by a bilayer Heisenberg model on the fuzzy sphere. Using the fuzzy-sphere state-operator correspondence, we obtain boundary operator spectra, identify low-lying boundary primary operators, extract operator-product-expansion (OPE) data, and estimate the boundary central charges for both boundary conditions. For the normal boundary condition, the universal amplitudes $a_\sigma$ and $b_t$ extracted from one- and two-point functions agree quantitatively with Monte Carlo benchmarks where available. For both $N=2$ and $N=3$, we find a positive extraordinary-log exponent $\alpha$, providing independent microscopic evidence for extraordinary-log boundary criticality. Our results extend fuzzy-sphere BCFT spectroscopy beyond the Ising universality class to continuous $O(N)$ symmetry.