Towards a categorification of scattering amplitudes
Abstract
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 pseudoperiodic categories. An algorithm to obtain the projectives of hearts of intermediate $t$structures for these types is presented.
 Publication:

arXiv eprints
 Pub Date:
 December 2021
 DOI:
 10.48550/arXiv.2112.14288
 arXiv:
 arXiv:2112.14288
 Bibcode:
 2021arXiv211214288B
 Keywords:

 High Energy Physics  Theory;
 Mathematical Physics;
 Mathematics  Representation Theory;
 81T18;
 81U20;
 16G70;
 13F60
 EPrint:
 33 pages, 14 figures, comments are very welcome, v2 fixed Fig. 3