On non-commutative open string theories

We investigate new compactifications of OM theory giving rise to a (3+1)-di mensional open string theory with non-commutative x(0)-x(1) and x(2)-x(3) c oordinates. The theory can be directly obtained by starting with a D3-brane with parallel (near critical) electric and magnetic field components, in t he presence of a RR scalar field. The magnetic parameter permits to interpo late continuously between the x(0)-x(1) non-commutative open string theory and the x(2)-x(3) spatial non-commutative U(N) super Yang-Mills theory. We discuss SL(2, Z) transformations of this theory. Using the supergravity des cription of the large-N limit, we also compute corrections to the quark-ant iquark Coulomb potential arising in the NCOS theory.