Towards a categorification of scattering amplitudes

Understand

Categorification of scattering amplitudes for planar Feynman diagrams in scalar field theories with a polynomial potential is reported.

• Amplitudes for cubic theories are directly written down in terms of projectives of hearts of intermediate $t$-structures restricted to the cluster category of quiver representations, without recourse to geometry.
• It is shown that for theories with $\phi^{m+2}$ potentials those corresponding to $m$-cluster categories are to be used.
• The case of generic polynomial potentials is treated and our results suggest the existence of a generalization of higher cluster categories which we call pseudo-periodic categories.