Studying 3D O(N) Surface CFT on the Fuzzy Sphere
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| Format: | Preprint |
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2026
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| _version_ | 1866914500703158272 |
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| author | Feng, Jiechao Wang, Taige |
| author_facet | Feng, Jiechao Wang, Taige |
| contents | 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 $a_σ$ 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 $α$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_21091 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Studying 3D O(N) Surface CFT on the Fuzzy Sphere Feng, Jiechao Wang, Taige Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Theory 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 $a_σ$ 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 $α$, 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. |
| title | Studying 3D O(N) Surface CFT on the Fuzzy Sphere |
| topic | Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2604.21091 |