Title: Large $n$: scattering amplitudes at large multiplicity

Abstract: What happens when we scatter a large number $n$ of particles, say with $n = 10^1000$? This question is out of reach of all existing approaches to scattering amplitudes, whether directly through Feynman diagrams or recursion relations. In this talk, I will study this problem at tree-level for a simple scalar theory, Tr($\phi^3$) theory, and describe a new way of accessing this regime, starting from the “tropical” representation of the amplitudes given by the formalism of surfaceology.  Remarkably, we find that at large $n$ the sum over diagrams “smooths out”. Working at leading order in $n$, and in certain “positive” regions of kinematic space, the final answer is astonishingly simple, given by a single term, determined by an optimization problem associated with a biased random walk. I will also describe a transformation from the tropical representation to a new “dual” theory for amplitudes, which in simple limits reduces to the motion of a particle on a half-line, evolving for a “time” $n$, allowing us to systematically extract the $1/n$ expansion of the amplitude. I will end by explaining how these results generalize to other large $n$ contexts, from the scattering of pions, to string scattering at ultra-high energies.

https://lbnl.zoom.us/j/94928022788?pwd=emVQWG1mTnhSbHVqekVuenk0VEVQZz09