Effective String Tension and Renormalizability: String Theory in a Noncommutative Space

TL;DR

This paper investigates how constant background fields modify string amplitudes, revealing an effective string tension increase, noncommutativity effects, and insights into renormalizability and UV-IR relations in noncommutative string theory.

Contribution

It derives phase functions for string scattering amplitudes in a noncommutative background, clarifies the regimes of momentum transfer, and discusses implications for renormalizability and UV-IR correspondence.

Findings

Effective string tension is larger than the fundamental tension.

Noncommutativity parameters influence phase functions in amplitudes.

Renormalizability remains unaffected by noncommutativity parameters.

Abstract

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 appearance of antisymmetric and symmetric noncommutativity parameters. We derive the form of the phase functions normalizing planar and nonplanar tachyon scattering amplitudes in this background, verifying the decoupling of the closed string sector in the regime of infinite momentum transfer. We show that the functional dependence of the phase functions on the antisymmetric star product of external momenta permits interpretation as a finite wavefunction renormalization of vertex operators in the open string sector. Using world-sheet duality we clarify the regimes of finite and zero momentum transfer between boundaries, demonstrating the existence of poles in the nonplanar amplitude when the momentum transfer equals the mass of an on-shell closed string state. Neither noncommutativity parameter has any impact on the renormalizability 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.