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 pseudo-periodic categories. An algorithm to obtain the projectives of hearts of intermediate $t$-structures for these types is presented.
- Publication:
-
arXiv e-prints
- 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
- E-Print:
- 33 pages, 14 figures, comments are very welcome, v2 fixed Fig. 3