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.
Transferring homotopy commutative algebraic structures
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abstract
We show that the sum over planar trees formula of Kontsevich and Soibelman transfers C-infinity structures along a contraction. Applying this result to a cosimplicial commutative algebra A^* over a field of characteristic zero, we exhibit a canonical unital C-infinity structure on Tot(A^*), which is unital if A^* is; in particular, we obtain a canonical C-infinity structure on the cochain complex of a simplicial set.
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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.