A Distance Conjecture for Branes

We use branes to generalize the Distance Conjecture. We conjecture that in any infinite-distance limit in the moduli space of a d-dimensional quantum gravity theory, among the set of particle towers and fundamental branes with at most pₘax≤ d-2 spacetime dimensions, at least one has mass/tension decreasing exponentially T~ exp(-αΔ) with the moduli space distance Δ at a rate of at least α≥ 1/√d-pₘax-1. Since pₘax can vary, this represents multiple conditions, where the Sharpened Distance Conjecture is the pₘax=1 case. This conjecture is a necessary condition imposed on higher-dimensional theories in order for the Sharpened Distance Conjecture to hold in lower-dimensional theories. We test our conjecture in theories with maximal and half-maximal supersymmetry in diverse dimensions, finding that it is satisfied and often saturated. In some cases where it is saturated -- most notably, heterotic string theory in 10 dimensions -- we argue that novel, low-tension non-supersymmetric branes must exist. We also identify patterns relating the rates at which various brane tensions vary in infinite-distance limits and relate these tensions to the species scale.