Noncommutative and ordinary super Yang-Mills on (D(p-2), Dp) bound states

We study properties of (D(p - 2), Dp) nonthreshold bound states (2 less than or equal to p less than or equal to 6) in the dual gravity description. These bound states can be viewed as Dp-branes with a nonzero NS B-field of rank two. We find that in the decoupling limit, the thermodynamics of the Np coincident Dp-branes with B-field is the same not only as that of Np coincident Dp-branes without B-field, but also as that of the Np-2 coincident D(p - 2)-branes with two smeared coordinates and no B-field, for Np-2/N-p = (V) over tilde(2)/[(2 pi)(2)(b) over tilde] with (V) over tilde(2) being the area of the two smeared directions and (b) over tilde a noncommutativity parameter. We also obtain the same relation from the thermodynamics and dynamics by probe methods. This suggests that the noncommutative super Yang-Mills with gauge group U(N-p) in (p + 1) dimensions is equivalent to an ordinary one with gauge group U(infinity) in (p - 1) dimensions in the limit (V) over tilde(2) -->infinity. We also find that the free energy of a Dp-brane probe with B-field in the background of Dp-branes with B-field coincides with that of a Dp-brane probe in the background of Dp-branes without B-field.