Noncommutative and Ordinary Super Yang-Mills on (D$(p-2)$, D$p$) Bound States

Rong-Gen Cai; Nobuyoshi Ohta

doi:10.1088/1126-6708/2000/03/009

paper

Noncommutative and Ordinary Super Yang-Mills on (D $(p - 2)$ , D $p$ ) Bound States

arXiv:hep-th/0001213 · doi:10.1088/1126-6708/2000/03/009

Abstract

We study properties of (D $(p - 2)$ , D $p$ ) nonthreshold bound states ( $2 \leq p \leq 6$ ) in the dual gravity description. These bound states can be viewed as D $p$ -branes with a nonzero NS $B$ field of rank two. We find that in the decoupling limit, the thermodynamics of the $N_{p}$ coincident D $p$ -branes with $B$ field is the same not only as that of $N_{p}$ coincident D $p$ -branes without $B$ field, but also as that of the $N_{p - 2}$ coincident D $(p - 2)$ -branes with two smeared coordinates and no $B$ field, for $N_{p - 2} / N_{p} = V ~_{2} / [(2 π)^{2} b ~]$ with $V ~_{2}$ being the area of the two smeared directions and $b ~$ 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 $U (\infty)$ in ( $p - 1$ ) dimensions in the limit $V ~_{2} \to \infty$ . We also find that the free energy of a D $p$ -brane probe with $B$ field in the background of D $p$ -branes with $B$ field coincides with that of a D $p$ -brane probe in the background of D $p$ -branes without $B$ field.

28 pages, Latex, references added, to appear in JHEP

Noncommutative and Ordinary Super Yang-Mills on (D(p−2), Dp) Bound States

Abstract

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Noncommutative and Ordinary Super Yang-Mills on (D $(p - 2)$ , D $p$ ) Bound States