The topological form is the Pfaffian form

Journal article

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 and of \mathsf{GL}_{2n}(\Z) . 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.

Authors: Balduf, P-H; Hu, S

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: EMS Press
• Journal: Documenta Mathematica
• Publication date: 2025-12-11
• DOI: 10.4171/dm/1039
• EISSN: 1431-0643
• ISSN: 1431-0635
• Language: English