F , D 1 ) , D 3 ) Bound State , S - Duality and Noncommutative Open String / Yang - Mills Theory

We study decoupling limits and S-dualities for noncommutative open string/ Yang-Mills theory in a gravity setup by considering an SL(2, Z) invariant super-gravity solutions of the form ((F, D1), D3) bound state of type IIB string theory. This configuration can be regarded as D3-brane solution with both electric and magnetic fields turned on along one of the spatial directions of the brane and preserves half of the space-time supersymmetries of the string theory. Our study indicates that there exists a decoupling limit for which the resulting theory is an open string theory defined in a geometry with noncommutativity in both space-time and space-space directions. We study S-duality of this noncommutative open string (NCOS) and find that the same decoupling limit in the S-dual description gives rise to a space-space noncommutative Yang-Mills theory (NCYM). We also discuss independently the decoupling limit for NCYM in this D3 brane background. Here we find that S-duality of NCYM theory does not always give a NCOS theory. Instead, it can give an ordinary Yang-Mills with singular metric and infinitely large coupling. We also find that the open string coupling relation between the two S-duality related theories is modified such that S-duality of a strongly coupled open-string/Yang-Mills theory does not necessarily give a weakly coupled theory. The relevant gravity dual descriptions of NCOS/NCYM are also given.