UV Cascade in Classical Yang-Mills Theory

TL;DR

This paper investigates the real-time evolution of classical Yang-Mills theory with large infrared fields, confirming a energy cascade to higher momenta characterized by a specific scaling solution, and analyzing the behavior of large occupancies.

Contribution

It provides the first lattice confirmation of a specific energy cascade scaling solution in classical Yang-Mills theory with large initial infrared fields.

Findings

Energy cascades to higher momenta with a scaling solution

Occupancy falls exponentially above a characteristic scale

No evidence for alternative infrared exponents or higher infrared occupancies

Abstract

We study the real-time behavior of classical Yang-Mills theory under initial conditions with nonperturbatively large, infrared field amplitudes. Our lattice study confirms the cascade of energy towards higher momenta and lower occupancy, which occurs via a scaling solution $f[p,t_1] = (t_0/t_1)^{4/7}\, f[p (t_0/t_1)^{1/7},t_0]$. Above a characteristic scale p_{max}, f falls exponentially; below p_{max}, $f[p] \propto p^{-4/3}$. We find no evidence for different infrared exponents or for infrared occupancies in excess of those described by this scaling solution. We also investigate what the fate of large occupancies would be, both in the electric and the magnetic sector.