On the Higher Categorical Structure of Topological Defects in Quantum Field Theories
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918013057368064 |
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| author | Müller, Lukas |
| author_facet | Müller, Lukas |
| contents | We propose a unifying mathematical framework describing the higher categorical structures formed by topological defects in quantum field theory equipped with tangential structures, such as orientations, framings, or $\operatorname{Pin}^{\pm}$-structures, in terms of structured versions of higher dagger categories. This recovers all previously known results, including the description of oriented topological defects in 2-dimensional quantum field theories by pivotal bicategories. Assuming the stratified cobordism hypothesis, we prove our proposal for topological defects with stable tangential structures that admit a direct sum in fully extended topological quantum field theories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_04761 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Higher Categorical Structure of Topological Defects in Quantum Field Theories Müller, Lukas Mathematical Physics High Energy Physics - Theory Algebraic Topology Category Theory Quantum Algebra We propose a unifying mathematical framework describing the higher categorical structures formed by topological defects in quantum field theory equipped with tangential structures, such as orientations, framings, or $\operatorname{Pin}^{\pm}$-structures, in terms of structured versions of higher dagger categories. This recovers all previously known results, including the description of oriented topological defects in 2-dimensional quantum field theories by pivotal bicategories. Assuming the stratified cobordism hypothesis, we prove our proposal for topological defects with stable tangential structures that admit a direct sum in fully extended topological quantum field theories. |
| title | On the Higher Categorical Structure of Topological Defects in Quantum Field Theories |
| topic | Mathematical Physics High Energy Physics - Theory Algebraic Topology Category Theory Quantum Algebra |
| url | https://arxiv.org/abs/2505.04761 |