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

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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.

fields

hep-th 1

years

2026 1

verdicts

UNVERDICTED 1

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  • Boundary criticality in the Gross-Neveu-Yukawa model at higher orders hep-th · 2026-06-05 · unverdicted · none · ref 36 · internal anchor

    Higher-order large-N and epsilon-expansion calculations of boundary free energies, fermion dimensions, and central charge in the Gross-Neveu-Yukawa universality class, with consistency checks between methods.