Multiloop noncommutative open string theory and their QFT limit

The multiloop amplitudes for open bosonic string in the presence of a const ant B-fieid are derived from first principles. The basic ingredients of the construction are the commutation relations for the string modes and the Re ggeon vertex describing the interaction among three generic string states. The modifications due to the presence of the B-Field affect nontrivially on ly the zero modes. This makes it possible to write in a simple and elegant way the general expression for multiloop string amplitudes in the presence of a constant B-field. The field theory limit of these string amplitudes is also considered. We show that it reproduces exactly the Feynman diagrams o f noncommutative field theories. Issues of uv/ir are briefly discussed.