Lower Bound for the Multi-Field Bounce Action

We present a lower bound for the multi-field bounce action with a quartic potential in the absence of gravity. We find that for a large number of fields the lower bound decreases with the number of fields as N^{-3}. This work clarifies previous statements made in numerical studies which found that the bounce action scales as N^{-2.66} and discusses some subtleties of studying field space trajectories.