Speaker
Description
Tropical field theory is a limit of quantum field theory where the spacetime dimension and the propagator power simultaneously approach zero. This can equivalently be viewed as a specific limit of Mellin transforms of all Feynman integrals of the theory, where they become simple rational functions of a dimensional regulator. These tropicalized Feynman integrals retain much of the combinatorial structure of UV subdivergences of the original theory, and there is strong numerical correlation between tropical and non-tropical theory. The special case of tropical subdivergence-free diagrams amounts to the Hepp bound (1908.09820), which has already found interesting applications for the study of Feynman integrals.
My talk is about the full amplitudes of tropical phi^4 theory at zero momentum transfer, including all Feynman integrals with subdivergences. These amplitudes can be computed efficiently from a combinatorial recurrence, which takes the form of a partial differential equation discovered by Michael Borinsky (2508.14263). Renormalization involves the usual combinatorics of subdiagram subtractions. By now, we know the exact renormalized perturbation series of tropical phi^4 theory to more than 200 loops, this allows to explicitly determine its asymptotic and non-perturbative structure, such as growth rates of the beta function or locations of singularities in the Borel plane. In particular, the data empirically answers the old questions of whether renormalons obstruct Borel-resummability of the beta function.
