Abstract: The relationship between representation theory and the study of scattering amplitudes for scalar field theories started with the work of Arkani-Hamed, Bai, He and Yan, when they showed that the amplitudes for planar scalar field theories with cubic potential can be calculated as the volume of a realisation of the associahedron. This connection was further developed by Bazier-Matte, Douville, Mousavand, Thomas and Yildrim, and subsequently by Padrol, Palu, Pilaud and Plamondon.

In this talk we propose a new combinatorial method for the calculation of scattering amplitudes for arbitrary planar field theories using the silting objects in the derived category of the category of representations of the linearly oriented A_n quiver. In particular, we show that this method applied to the monomial φ^(m+2) potentials recovers the Auslander-Reiten quiver of the m-cluster category of type A_n. This talk is based on a joint work with S. Barmeier, P. Oak, A. Pal and K. Ray. https://arxiv.org/abs/2112.14288