D-branes and Short Distances in String Theory

We study the behavior of D-branes at distances far shorter than the string length scale ls. We argue that short-distance phenomena are described by the IR behavior of the Dbrane world-volume quantum theory. This description is valid until the brane motion becomes relativistic. At weak string coupling gs this corresponds to momenta and energies far above string scale. We use 0-brane quantum mechanics to study 0-brane collisions and find structure at length scales corresponding to the eleven-dimensional Planck length (l P ∼ g 1/3 s ls) and to the radius of the eleventh dimension in M-theory (R11 ∼ gsls). We use 0-branes to probe non-trivial geometries and topologies at sub-stringy scales. We study the 0-brane 4-brane system, calculating the 0-brane moduli space metric, and find the bound state at threshold, which has characteristic size l P . We examine the blowup of an orbifold and are able to resolve the resulting S down to size l P . A 0-brane with momentum approaching 1/R11 is able to explore a larger configuration space in which the blowup is embedded. Analogous phenomena occur for small instantons. We finally turn to 1-branes and calculate the size of a bound state to be ∼ g s ls, the 1-brane tension scale.