Field theory of $\mathfrak{su}(n)$: the absence of non-zero scatterings
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| Format: | Preprint |
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2026
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| _version_ | 1866916045310132224 |
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| author | Boffo, Eugenia Pulmann, Ján Ravas, Ľuboš |
| author_facet | Boffo, Eugenia Pulmann, Ján Ravas, Ľuboš |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_26024 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Field theory of $\mathfrak{su}(n)$: the absence of non-zero scatterings Boffo, Eugenia Pulmann, Ján Ravas, Ľuboš Mathematical Physics High Energy Physics - Theory K-Theory and Homology 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. |
| title | Field theory of $\mathfrak{su}(n)$: the absence of non-zero scatterings |
| topic | Mathematical Physics High Energy Physics - Theory K-Theory and Homology |
| url | https://arxiv.org/abs/2605.26024 |