Multiloop Noncommutative Open String Theory and their QFT limit

TL;DR

This paper derives multiloop open string amplitudes with a B-field, showing their field theory limit reproduces noncommutative QFT diagrams and discussing UV/IR issues.

Contribution

It provides a first-principles derivation of multiloop amplitudes in noncommutative open string theory with a B-field, highlighting the zero mode modifications.

Findings

Multiloop string amplitudes are explicitly derived with B-field effects.

The field theory limit reproduces noncommutative QFT Feynman diagrams.

UV/IR mixing issues are briefly discussed.

Abstract

The multiloop amplitudes for open bosonic string in presence of a constant B-field are derived from first principles. The basic ingredients of the construction are the commutation relations for the string modes and the Reggeon vertex describing the interaction among three generic string states. The modifications due to the presence of the B-field affect non--trivially only the zero modes. This makes it possible to write in a simple and elegant way the general expression for multiloop string amplitudes in 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 of noncommutative field theories. Issues of UV/IR are briefly discussed.