The charge radius of a Dpbrane

Sen has shown that tachyon condensation in Dbrane--anti-Dbrane configurations can lead to remarkable connections between string theories. A consequence of his results is that there is a minimal value of the radial coordinate $r_{c} \propto \sqrt{\alpha'} g^{1/(9-p)}$ such that Dpbrane charge cannot be localized to values smaller than $r_{c}.$ At this value of $r_{c}$ the curvature and the gradient of the Ramond-Ramond field strength are of order $1/\alpha'.$ For small $g$ the shortest value of $r$ that can be probed by a D0brane is $g^{1/9}\sqrt{\alpha'}\gg g^{1/3}\sqrt{\alpha'} \equiv \ell_{11},$ where $\ell_{11}$ is the Planck length in eleven dimensions. For $p=3,$ the critical radial coordinate for a tachyonic mode to develop for a configuration of $N$ D3branes scales as $(gN)^{{1/6}}\sqrt{\alpha'}.$