The Topological form is the Pfaffian form
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866912271297413120 |
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| author | Balduf, Paul-Hermann Hu, Simone |
| author_facet | Balduf, Paul-Hermann Hu, Simone |
| contents | For a given graph $G$, Budzik, Gaiotto, Kulp, Wang, Williams, Wu, Yu, and the first author studied a ''topological'' differential form $α_G$, which expresses violations of BRST-closedness of a quantum field theory along a single topological direction. In a seemingly unrelated context, Brown, Panzer, and the second author studied a ''Pfaffian'' differential form $ϕ_G$, which is used to construct cohomology classes of the odd commutative graph complex. We give an explicit combinatorial proof that $α_G$ coincides with $ϕ_G$. We also discuss the equivalence of several properties of these forms, which had been established independently for both contexts in previous work. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_09558 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Topological form is the Pfaffian form Balduf, Paul-Hermann Hu, Simone Mathematical Physics Combinatorics Quantum Algebra 81T18, 81Q30, 05C31, 18G85, 53D55, 81T50, 81T45 For a given graph $G$, Budzik, Gaiotto, Kulp, Wang, Williams, Wu, Yu, and the first author studied a ''topological'' differential form $α_G$, which expresses violations of BRST-closedness of a quantum field theory along a single topological direction. In a seemingly unrelated context, Brown, Panzer, and the second author studied a ''Pfaffian'' differential form $ϕ_G$, which is used to construct cohomology classes of the odd commutative graph complex. We give an explicit combinatorial proof that $α_G$ coincides with $ϕ_G$. We also discuss the equivalence of several properties of these forms, which had been established independently for both contexts in previous work. |
| title | The Topological form is the Pfaffian form |
| topic | Mathematical Physics Combinatorics Quantum Algebra 81T18, 81Q30, 05C31, 18G85, 53D55, 81T50, 81T45 |
| url | https://arxiv.org/abs/2503.09558 |