(F1, D1, D3) bound state, its scaling limits and SL(2, Z) duality

We discuss the properties of the bound state (F1, D1, D3) in IIB supergravi ty in three different scaling limits and the SL(2,Z) transformation of the resulting theories. In the simple decoupling limit with finite electric and magnetic components of NS B field, the worldvolume theory is the N = 4 sup er Yang-Mills (SYM) and the supergravity dual is still the AdS(5) x S-5. In the large magnetic field limit with finite electric field, the theory is t he noncommutative super Yang-Mills (NCSYM), and the supergravity dual is th e same as that without the electric background. We show; how to take the de coupling limit of the closed string for the critical electric background an d finite magnetic field, and that the resulting theory is the noncommutativ e open string (NCOS) with both space-time and space-space noncommutativitie s. It is shown that under the SL(2, Z) transformation, the SYM becomes itse lf with a different coupling constant, the NCSYM is mapped to a NCOS, and t he NCOS in general transforms into another NCOS and reduces to a NCSYM in a special case.