On the structure of higher-dimensional integrable field theories
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866914512597155840 |
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| author | Benini, Marco Cullinan, Ryan A. Schenkel, Alexander Vicedo, Benoit |
| author_facet | Benini, Marco Cullinan, Ryan A. Schenkel, Alexander Vicedo, Benoit |
| contents | We propose a general framework for integrable field theories in arbitrary spacetime dimension $d+1$ which is based on $d$-term $L_\infty$-algebras. Specifically, we introduce cyclic $L_\infty$-algebras describing topological-holomorphic higher Chern-Simons theories on $M \times \mathbb{C}P^1$ with suitable singularity structures and boundary conditions, controlled by a meromorphic $1$-form on $\mathbb{C}P^1$. Using homological perturbation theory and homotopy transfer, we construct weakly equivalent models describing $(d+1)$-dimensional field theories on $M$. Their integrability is witnessed by a natural map to an $L_\infty$-algebra describing higher Lax connections, yielding conserved charges associated with higher-dimensional cycles in $M$. The resulting theories admit natural action functionals and recover the Costello-Yamazaki construction in $2$ dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_24864 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the structure of higher-dimensional integrable field theories Benini, Marco Cullinan, Ryan A. Schenkel, Alexander Vicedo, Benoit High Energy Physics - Theory Mathematical Physics 70Sxx, 81Txx, 55Uxx We propose a general framework for integrable field theories in arbitrary spacetime dimension $d+1$ which is based on $d$-term $L_\infty$-algebras. Specifically, we introduce cyclic $L_\infty$-algebras describing topological-holomorphic higher Chern-Simons theories on $M \times \mathbb{C}P^1$ with suitable singularity structures and boundary conditions, controlled by a meromorphic $1$-form on $\mathbb{C}P^1$. Using homological perturbation theory and homotopy transfer, we construct weakly equivalent models describing $(d+1)$-dimensional field theories on $M$. Their integrability is witnessed by a natural map to an $L_\infty$-algebra describing higher Lax connections, yielding conserved charges associated with higher-dimensional cycles in $M$. The resulting theories admit natural action functionals and recover the Costello-Yamazaki construction in $2$ dimensions. |
| title | On the structure of higher-dimensional integrable field theories |
| topic | High Energy Physics - Theory Mathematical Physics 70Sxx, 81Txx, 55Uxx |
| url | https://arxiv.org/abs/2604.24864 |