Holography and D 3 - branes in Melvin Universes

Recently,in a paper hep-th/0511197, it was found that non-commutative super Yang-Mills (NCSYM) theory with space-dependent noncommutativity can be formulated as a decoupling limit of open strings ending on D3-branes wrapping a Melvin universe supported by a flux of the NSNS B-field. Under S-duality, we show that this theory turns into a noncommutative open string (NCOS) theory with space-dependent space-time noncommutativity and effective spacedependent string scale. It is an NCOS theory with both space-dependent space-space and spacetime noncommutativities under more general SL(2,Z) transformation. These space-dependent noncommutative theories (NCSYM and NCOS) have completely the same thermodynamics as that of ordinary super YM theory, NCSYM and NCOS theories with constant noncommutativity in the dual supergravity description. Starting from black D3-brane solution in the Melvin universe and making a Lorentz boost along one of spatial directions on the worldvolume of D3branes, we show that the decoupled theory is a light-like NCSYM theory with space-dependent noncommutativity in a static frame or in an infinite-momentum frame depending on whether there is a gravitational pp-wave on the worldvolume of the D3-branes. Email address: [email protected] Email address: [email protected]. Address after 31 March 2006: Department of Physics, Kinki University, Higashi-Osaka, Osaka 577-8502,Japan