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where φ is the dilaton field, F$_{p}$$_{+2}$ is a p +2 form field strength, and l$_{s}$ is the string length; the string length l$_{s}$ is related to the string tension (2 πα $^{′}$)− 1 by l 2 s = α $^{′}$. This form is suggestive of the result G (10) N = 8 π $^{6}$g2 $_{s}$l 8 s [320], where g$_{s}$ is given by the vacuum expectation value of the dilaton field, g$_{s}$ = exp( φ ). Just as a 0 dimensional point charge sources a 1 form potential A which creates a 2 form field strength F = dA in E&M, this p + 2 form is sourced by a p dimensional object, a p brane. Similarly to E&M, setting a spherically symmetric charge at the origin the integral of the flux of the p + 2 form yields the charge: 

<img src='content_image/308543.jpg'>

Extremizing the above action for a p brane with the p parallel dimensions denoted by x $^{i}$, the radial distance away from the p brane denoted by ρ , and the angular dimensions encoded in d Ω, yields the metric 

<img src='content_image/308544.jpg'>

<img src='content_image/308545.jpg'>

<img src='content_image/308546.jpg'>

