The authors prove the absence of non-zero trivalent tree-level scattering amplitudes in su(n) field theory toy models via homological perturbation theory and demonstrate non-trivial higher products in an enlarged field space.
Hochschild-Pirashvili homology on suspensions and representations of $Out(F_n)$
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abstract
We show that the Hochschild-Pirashvili homology on any suspension admits the so called Hodge splitting. For a map between suspensions $f\colon \Sigma Y\to \Sigma Z$, the induced map in the Hochschild-Pirashvili homology preserves this splitting if $f$ is a suspension. If $f$ is not a suspension, we show that the splitting is preserved only as a filtration. As a special case, we obtain that the Hochschild-Pirashvili homology on wedges of circles produces new representations of $Out(F_n)$ that do not factor in general through $GL(n,Z)$. The obtained representations are naturally filtered in such a way that the action on the graded quotients does factor through $GL(n,Z)$.
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math-ph 1years
2026 1verdicts
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Field theory of $\mathfrak{su}(n)$: the absence of non-zero scatterings
The authors prove the absence of non-zero trivalent tree-level scattering amplitudes in su(n) field theory toy models via homological perturbation theory and demonstrate non-trivial higher products in an enlarged field space.