Giant Leaps and Minimal Branes in Multi-Dimensional Flux Landscapes

There is a standard story about decay in multi-dimensional flux landscapes: that from any state, the fastest decay is to take a small step, discharging one flux unit at a time; that fluxes with the same coupling constant are interchangeable; and that states with N units of a given flux have the same decay rate as those with -N. We show that this standard story is false. The fastest decay is a giant leap that discharges many different fluxes in unison; this decay is mediated by a 'minimal' brane that wraps the internal manifold and exhibits behavior not visible in the effective theory. We discuss the implications for the cosmological constant.