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arXiv · 2503.09558

The Topological form is the Pfaffian form

Paul-Hermann Balduf·Simone Hu
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Abstract

For a given graph $G$, Budzik, Gaiotto, Kulp, Wang, Williams, Wu, Yu, and the first author studied a ''topological'' differential form $\alpha_G$, 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 $\phi_G$, which is used to construct cohomology classes of the odd commutative graph complex. We give an explicit combinatorial proof that $\alpha_G$ coincides with $\phi_G$. We also discuss the equivalence of several properties of these forms, which had been established independently for both contexts in previous work.

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Paul-Hermann Balduf, Simone Hu. 2025-03-12. The Topological form is the Pfaffian form. https://arxiv.org/abs/2503.09558

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