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arXiv · 2605.26024

Field theory of $\mathfrak{su}(n)$: the absence of non-zero scatterings

Eugenia Boffo·Ján Pulmann·Ľuboš Ravas
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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--Mn\"{e}v to arbitrary $n$. In contrast to this, we show how to obtain non-trivial higher products when transferring to a larger space of fields.

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Eugenia Boffo, Ján Pulmann, Ľuboš Ravas. 2026-05-25. Field theory of $\mathfrak{su}(n)$: the absence of non-zero scatterings. https://arxiv.org/abs/2605.26024

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