D-branes and short distances in string theory

We study the behavior of D-branes at distances far shorter than the string length scale l(s). We argue that short-distance phenomena are described by the IR behavior of the D-brane world-volume quantum theory. This description is valid until the brane motion becomes relativistic. At weak string coupling g(s) 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 (lp(11) similar to g(s)(1/3)l(s)) and to the radius of the eleventh dimension in M-theory (R(11) similar to g(s)l(s)). 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 lp(11). We examine the blowup of an orbifold and are able to resolve the resulting S-2 down to size lp(11). A 0-brane with momentum approaching 1/R(11) 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 similar to g(s)(1/2)l(s), the 1-brane tension scale.