Toral Chern-Simons TQFT via Geometric Quantization in Real Polarization
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866912995756474368 |
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| author | Galviz, Daniel |
| author_facet | Galviz, Daniel |
| contents | We construct toral Chern-Simons theory with gauge group $\mathbb T=\mathfrak t/Λ\cong U(1)^n$ from an even, integral, nondegenerate symmetric bilinear form $K:Λ\timesΛ\to\mathbb Z$ by geometric quantization via real polarization. We obtain a unitary extended $(2+1)$-dimensional TQFT by constructing the boundary state spaces and canonical operators and proving that they satisfy the cylinder and gluing axioms. The finite discriminant group $G_K=Λ^*/KΛ$ arises naturally in the theory and controls the genus-$g$ state spaces. At genus one, the theory recovers the finite quadratic data underlying bosonic Abelian topological order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_01016 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Toral Chern-Simons TQFT via Geometric Quantization in Real Polarization Galviz, Daniel Mathematical Physics Strongly Correlated Electrons High Energy Physics - Theory Quantum Algebra We construct toral Chern-Simons theory with gauge group $\mathbb T=\mathfrak t/Λ\cong U(1)^n$ from an even, integral, nondegenerate symmetric bilinear form $K:Λ\timesΛ\to\mathbb Z$ by geometric quantization via real polarization. We obtain a unitary extended $(2+1)$-dimensional TQFT by constructing the boundary state spaces and canonical operators and proving that they satisfy the cylinder and gluing axioms. The finite discriminant group $G_K=Λ^*/KΛ$ arises naturally in the theory and controls the genus-$g$ state spaces. At genus one, the theory recovers the finite quadratic data underlying bosonic Abelian topological order. |
| title | Toral Chern-Simons TQFT via Geometric Quantization in Real Polarization |
| topic | Mathematical Physics Strongly Correlated Electrons High Energy Physics - Theory Quantum Algebra |
| url | https://arxiv.org/abs/2604.01016 |