57 Chapter 2: Motivation we find the metric takes the form which we will find useful later on. Besides strings, string theory necessarily involves nonperturbative objects upon which open strings may end; these are D branes, D for Dirichlet, or Figure 2.12: (a) Open strings ending on a D brane. (b) D branes as the source of closed strings. Figure adapted from [322]. D branes and Chan-Paton Factors ds 2 = 1 $^{√}$H ( r ) ( − dt 2 + p ∑ i =1 dx $^{i}$dxi ) + $^{√}$H ( r ) $^{(}$dr 2 + r $^{2}$d Ω 2 8 − p $^{)}$; (2.38) e − 2 φ = 1 g 2 s H ( r ) 3 − p 4 , (2.39) H ( r ) = 1 f$_{+}$ ( ρ ) = 1 + ( r$_{+}$ r ) 7 − p , (2.40) r 7 − p + = g$_{s}$d$_{p}$Nl 7 − p s , (2.41) (a) (b)