Brane Solutions

Abstract

In the (NS, NS)-sector, we have the explicit solution given by the fundamental string for $d=10$, $n=3$

$$\begin{aligned} ds_E^2 = \left( 1+ \frac{\alpha }{r^6} \right) ^{-3/4} dx_{\mu }^2 + \left( 1+ \frac{\alpha }{r^6} \right) ^{1/4} dy_n^2 ,~~~ e^{\Phi } = \left( 1+ \frac{\alpha }{r^6} \right) ^{-1/2} \sim g_s ~. \end{aligned}$$