String-tension interpretation of BIon energy
= String-tension interpretation of BIon energy
{title2=$\Delta E=4\pi T_3c\,(X_{\rm cut}-X_\infty)$}
For $X-X_\infty=c/r$, subtracting the planar <D3-brane> energy leaves $T_3\int|\nabla X|^2d^3x=4\pi T_3c^2/r_0$ outside a cutoff. Since $X_{\rm cut}-X_\infty=c/r_0$, its coefficient is the carried string tension. Electric charge quantization gives $c=\pi g_s|N|\alpha'$ and coefficient $|N|T_{F1}$; magnetic charge gives $c=\pi|N|\alpha'$ and coefficient $|N|T_{D1}$.