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The main difference is that the zero modes of open strings with Dirichlet boundary conditions in some directions are not dynamical and the low-energy fields corresponding to the massless modes of the open superstring are arranged into representations of SO(1, p). The vector components along directions with Dirichlet boundary conditions become scalars and we are left with a vector Aµ with components along the directions which have Neumann boundary conditions. These fields are the bosonic components of a vector supermultiplet in (p + 1) dimensions.

75) B = tan ϕ fp−1 hp dxp−1 ∧ dxp , and is charged under RR field strengths, F (p) and F (p+2) . The components along the directions parallel to the bound state are (p) Fx0 ,x1 ,···,xp−2 ,r = sin ϕ ∂r fp−1 , (p+2) Fx0 ,x1 ,···,xp ,r = cos ϕ hp ∂r fp−1 . e. F (p) = ∗ F (10−p) for p ≤ 5. In particular this implies that F (5) is self-dual, as is well-known for the type IIB theory. It is clear from the above equations that for ϕ = 0 the (D(p-2),Dp) solution reduces to the Dp-brane geometry whereas for ϕ = π/2 it becomes a D(p-2)-brane smeared along the xp−1 xp directions.

The string frame metric and dilaton for this bound state are [16] ds2 = fp−1/2 hp−1/2 − ( dx0 )2 + ( dx1 )2 + hp ( dx2 )2 + . . + ( dxp )2 + + fp1/2 hp−1/2 dr 2 + r 2 dΩ28−p , ˜ 3−p p−5 eφ = fp 4 hp 4 . 89) The Dp-brane of the background extends along the directions x0 · · · xp , whereas the F1 component lies along x0 x1 . 79). 77) for the (D(p-2),Dp) bound state. 79). (M2,M5) bound state There are also solutions of eleven-dimensional supergravity carrying more than one charge as the ones of ten-dimensional supergravities corresponding to bound states of branes.

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