D-brane dynamics

I calculate the semiclassical phase shift (δ), as function of impact parameter (b) and velocity (ν), when one D-brane moves past another. From its low-velocity expansion I show that, for torroidal compactifications, the moduli space of two identical D-branes stays flat to all orders in α′. For K3 compactifications, the calculation of the D-brane moduli-space metric can be mapped to a dual gauge-coupling renormalization problem. In the ultrarelativistic regime, the absorptive part of the phase shift grows as if the D-branes were black disks of area ∼ α′ ln[1(1 − ν2)]. The scattering of large fundamental strings shares all the above qualitative features. A side remark concerns the intriguing duality between limiting electric fields and the speed of light.