Abstract

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 D-brane 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 11 P ∼ g1/3 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 l11 P. We examine the blowup of an orbifold and are able to resolve the resulting S2 down to size l11 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 1/2 s ls, the 1-brane tension scale. August