A Rigorous Functional-Integral Construction of Toral Chern-Simons Theory
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917380296278016 |
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| author | Galviz, Daniel |
| author_facet | Galviz, Daniel |
| contents | We construct the functional integral of Abelian Chern-Simons theory with toral gauge group $\mathbb T=\mathfrak t/Λ\cong U(1)^n$ at level $K$, where $K:Λ\timesΛ\to\mathbb Z$ is an even, integral, nondegenerate symmetric bilinear form, by exact zeta-regularized Gaussian evaluation of the formal quotient integral over connections modulo gauge. For closed $3$-manifolds, this yields a topological invariant; for manifolds with boundary, the relative functional integral produces the canonical boundary state. The resulting theory satisfies the required axioms of a $(2+1)$-dimensional TQFT. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_02013 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Rigorous Functional-Integral Construction of Toral Chern-Simons Theory Galviz, Daniel Mathematical Physics High Energy Physics - Theory Quantum Algebra We construct the functional integral of Abelian Chern-Simons theory with toral gauge group $\mathbb T=\mathfrak t/Λ\cong U(1)^n$ at level $K$, where $K:Λ\timesΛ\to\mathbb Z$ is an even, integral, nondegenerate symmetric bilinear form, by exact zeta-regularized Gaussian evaluation of the formal quotient integral over connections modulo gauge. For closed $3$-manifolds, this yields a topological invariant; for manifolds with boundary, the relative functional integral produces the canonical boundary state. The resulting theory satisfies the required axioms of a $(2+1)$-dimensional TQFT. |
| title | A Rigorous Functional-Integral Construction of Toral Chern-Simons Theory |
| topic | Mathematical Physics High Energy Physics - Theory Quantum Algebra |
| url | https://arxiv.org/abs/2604.02013 |