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 a constant background two-form tensor field are characterized by an effective string tension larger than the fundamental string tension, and by the appe arance of antisymmetric and symmetric noncommutativity parameters. We deriv e the form of the phase functions normalizing planar and nonplanar tachyon scattering amplitudes in this background, verifying the decoupling of the c losed string sector in the regime of infinite momentum transfer. We show th at the functional dependence of the phase functions on the antisymmetric st ar product of external momenta permits interpretation as a finite wavefunct ion renormalization of vertex operators in the open string sector. Using wo rld-sheet duality we clarify the regimes of finite and zero momentum transf er between boundaries, demonstrating the existence of poles in the nonplana r amplitude when the momentum transfer equals the mass of an on-shell close d string state. Neither noncommutativity parameter has any impact on the re normalizability of open and closed string theory in the wilsonian sense. We comment on the relationship to noncommutative scalar field theory and the UV-IR correspondence.