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.
Remarks on Chern-Simons invariants
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abstract
The perturbative Chern-Simons theory is studied in a finite-dimensional version or assuming that the propagator satisfies certain properties (as is the case, e.g., with the propagator defined by Axelrod and Singer). It turns out that the effective BV action is a function on cohomology (with shifted degrees) that solves the quantum master equation and is defined modulo certain canonical transformations that can be characterized completely. Out of it one obtains invariants.
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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.