A Distance Conjecture for branes

A bstract 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 p max spacetime dimensions (where p max is an integer between 1 and d – 2), at least one has mass/tension decreasing exponentially T ~ exp(– α ∆) with the moduli space distance ∆ at a rate of at least α ≥ 1/ $$ \sqrt{d-{p}_{\textrm{max}}-1} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msqrt> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>−</mml:mo> <mml:msub> <mml:mi>p</mml:mi> <mml:mi>max</mml:mi> </mml:msub> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msqrt> </mml:math> . Since p max can vary, this represents multiple conditions, where the Sharpened Distance Conjecture is the p max = 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.