Lower bound for the multifield bounce action

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