Effective string tension and renormalizability: string theory in a noncommutative space

We show that the one loop amplitudes of open and closed string theory in aconstant background two-form tensor field are characterized by an effectivestring tension larger than the fundamental string tension, and by theappearance of antisymmetric and symmetric noncommutativity parameters. Wederive the form of the phase functions normalizing planar and nonplanar tachyonscattering amplitudes in this background, verifying the decoupling of theclosed string sector in the regime of infinite momentum transfer. We show thatthe functional dependence of the phase functions on the antisymmetric starproduct of external momenta permits interpretation as a finite wavefunctionrenormalization of vertex operators in the open string sector. Usingworld-sheet duality we clarify the regimes of finite and zero momentum transferbetween boundaries, demonstrating the existence of poles in the nonplanaramplitude when the momentum transfer equals the mass of an on-shell closedstring state. Neither noncommutativity parameter has any impact on therenormalizability of open and closed string theory in the Wilsonian sense. Wecomment on the relationship to noncommutative scalar field theory and the UV-IRcorrespondence.Comment: Added reference, version to appear in JHE