The charge radius of a Dpbrane

Sen has shown that tachyon condensation in Dbrane-anti-Dbrane configuration s can lead to remarkable connections between string theories. A consequence of his results is that there is a minimal value of the radial coordinate r (c) proportional to root alpha'(gN)(1/(9-p)) such that N units of Dpbrane c harge cannot be localized to values smaller than r(c). At this value of r(c ) the curvature is of order 1/alpha' and the gradient of the Ramond-Ramond field strength is of order 1/(alpha')(3/2), and the vacuum, regarded as a D -brane-anti-D-brane configuration with a tachyon condensate, is rendered un stable, leading to a separation of the D-brane and the anti-D-brane. This v alue of rc lies in the region intermediate between the near-horizon regime and the asymptotic regime for D-brane classical solutions for small g. This vacuum stability bound on the curvature can be interpreted as an uncertain ty relation for D-brane charge.