Speaker
Description
I will present joint work on the behavior of Feynman integrals and perturbative expansions at large loop orders. Using the tropical sampling algorithm for evaluating Feynman integrals, along with a dedicated graph-sampling algorithm to generate representative sets of Feynman diagrams, we computed approximately $10^7$ integrals with up to 17 loops in four-dimensional $\phi^4$ theory. Through maximum likelihood fits, we find that the values of these integrals at large loop order are distributed according to a log-gamma distribution. This empirical observation opens up a new avenue towards the large-order behavior in perturbative quantum field theory. Guided by instanton considerations, we extrapolate the primitive contribution to the $\phi^4$ beta function to all loop orders.
References
https://arxiv.org/abs/2503.07803
