Orbifolds, higher dagger structures, and idempotents
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866910243641884672 |
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| author | Carqueville, Nils Lüders, Tim |
| author_facet | Carqueville, Nils Lüders, Tim |
| contents | The orbifold/condensation completion procedure of defect topological quantum field theories can be seen as carrying out a lattice or state sum model construction internal to an ambient theory. In this paper, we propose a conceptual algebraic description of orbifolds/condensations for arbitrary tangential structures in terms of higher dagger structures and higher idempotents. In particular, we obtain (oriented) orbifold completion from (framed) condensation completion by using a general strictification procedure for higher dagger structures which we describe explicitly in low dimensions; we also discuss the spin and unoriented case. We provide several examples of higher dagger categories, such as those associated to state sum models, (orbifolds of) Landau--Ginzburg models, and truncated affine Rozansky--Witten models. We also explain how their higher dagger structures are naturally induced from rigid symmetric monoidal structures, recontextualizing and extending results from the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_17764 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Orbifolds, higher dagger structures, and idempotents Carqueville, Nils Lüders, Tim Quantum Algebra High Energy Physics - Theory Mathematical Physics Category Theory The orbifold/condensation completion procedure of defect topological quantum field theories can be seen as carrying out a lattice or state sum model construction internal to an ambient theory. In this paper, we propose a conceptual algebraic description of orbifolds/condensations for arbitrary tangential structures in terms of higher dagger structures and higher idempotents. In particular, we obtain (oriented) orbifold completion from (framed) condensation completion by using a general strictification procedure for higher dagger structures which we describe explicitly in low dimensions; we also discuss the spin and unoriented case. We provide several examples of higher dagger categories, such as those associated to state sum models, (orbifolds of) Landau--Ginzburg models, and truncated affine Rozansky--Witten models. We also explain how their higher dagger structures are naturally induced from rigid symmetric monoidal structures, recontextualizing and extending results from the literature. |
| title | Orbifolds, higher dagger structures, and idempotents |
| topic | Quantum Algebra High Energy Physics - Theory Mathematical Physics Category Theory |
| url | https://arxiv.org/abs/2504.17764 |