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 ≤ p ≤ 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/Np=V tilde2/[(2π)2b tilde] with V tilde2 being the area of the two smeared directions and b tilde a noncommutativity parameter. We also obtain the same relation from the thermodyanmics and dynamics by probe methods. This suggests that the noncommutative super Yang-Mills with gauge group U(Np) in (p + 1) dimensions is equivalent to an ordinary one with gauge group U(∞) in (p - 1) dimensions in the limit V tilde2 → ∞. 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. (author)