Abstract:We inspect $\mathfrak{su}(n)$ forms, providing greater detail for $n=2,3$, as a toy model for a field theory in finite dimensions and with gauge symmetries. Relying on homological perturbation theory, we show that there are no scattering amplitudes with trivalent tree-level diagrams, except for the interaction vertex, thus extending a known argument of Cattaneo--Mnëv to arbitrary $n$. In contrast to this, we show how to obtain non-trivial higher products when transferring to a larger space of fields.
| Comments: | Prepared for the Proceedings of Corfu Summer Institute 2025 "Schools and Workshops on Elementary Particle Physics and Gravity", 25 pages |
| Subjects: | Mathematical Physics (math-ph); High Energy Physics - Theory (hep-th); K-Theory and Homology (math.KT) |
| Cite as: | arXiv:2605.26024 [math-ph] |
| (or arXiv:2605.26024v1 [math-ph] for this version) | |
| https://doi.org/10.48550/arXiv.2605.26024 arXiv-issued DOI via DataCite (pending registration) |
From: Ľuboš Ravas [view email]
[v1]
Mon, 25 May 2026 16:45:20 UTC (53 KB)
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