Pivotal Module Categories, Factorization Homology and Modular Invariant Modified Traces
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866914216689008640 |
|---|---|
| author | Becerra, Jorge Woike, Lukas |
| author_facet | Becerra, Jorge Woike, Lukas |
| contents | The algebraic notion of a pivotal module category was developed by Schaumann and Shimizu and is central to the description of boundary conditions in conformal field theory according to a proposal by Fuchs and Schweigert. In this paper, we present a large class of examples of pivotal module categories of topological origin: For a unimodular finite ribbon category $\mathcal{A}$, we prove that the factorization homology $\int_Σ\mathcal{A}$ of a compact oriented surface $Σ$ with $n$ marked boundary intervals, at least one per connected component, comes with the structure of a pivotal module category over $\mathcal{A}^{\boxtimes n}$. This endows the internal skein algebras of Ben-Zvi-Brochier-Jordan, in particular the elliptic double, with a symmetric Frobenius structure. As application, we obtain, for each choice of $\mathcal{A}$, a family of full open conformal field theories, each of which comes with correlation functions for all surfaces with marked boundary intervals that are explicitly computable using factorization homology. As a further application, we explain how modified traces can be 'integrated' over surfaces: We show that the modified trace for $\mathcal{A}$ extends in a canonical way to the factorization homology of $Σ$. The resulting traces have the remarkable property of being modular invariant, i.e. fixed by the mapping class group action. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_19669 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pivotal Module Categories, Factorization Homology and Modular Invariant Modified Traces Becerra, Jorge Woike, Lukas Quantum Algebra Mathematical Physics Category Theory Representation Theory The algebraic notion of a pivotal module category was developed by Schaumann and Shimizu and is central to the description of boundary conditions in conformal field theory according to a proposal by Fuchs and Schweigert. In this paper, we present a large class of examples of pivotal module categories of topological origin: For a unimodular finite ribbon category $\mathcal{A}$, we prove that the factorization homology $\int_Σ\mathcal{A}$ of a compact oriented surface $Σ$ with $n$ marked boundary intervals, at least one per connected component, comes with the structure of a pivotal module category over $\mathcal{A}^{\boxtimes n}$. This endows the internal skein algebras of Ben-Zvi-Brochier-Jordan, in particular the elliptic double, with a symmetric Frobenius structure. As application, we obtain, for each choice of $\mathcal{A}$, a family of full open conformal field theories, each of which comes with correlation functions for all surfaces with marked boundary intervals that are explicitly computable using factorization homology. As a further application, we explain how modified traces can be 'integrated' over surfaces: We show that the modified trace for $\mathcal{A}$ extends in a canonical way to the factorization homology of $Σ$. The resulting traces have the remarkable property of being modular invariant, i.e. fixed by the mapping class group action. |
| title | Pivotal Module Categories, Factorization Homology and Modular Invariant Modified Traces |
| topic | Quantum Algebra Mathematical Physics Category Theory Representation Theory |
| url | https://arxiv.org/abs/2512.19669 |