UV/IR Mixing in Noncommutative Field Theory via Open String Loops

TL;DR

This paper demonstrates how open string loop amplitudes in a background B-field reproduce the UV/IR mixing phenomena of noncommutative field theories, revealing IR closed string modes responsible for singularities.

Contribution

It explicitly connects open string loop calculations with noncommutative field theory UV/IR mixing, confirming the survival of certain IR modes in the decoupling limit.

Findings

Nonplanar string amplitudes reproduce UV/IR mixing.

IR closed string modes cause IR singularities.

Results hold for both bosonic and supersymmetric strings.

Abstract

We explicitly evaluate one-loop (annulus) planar and nonplanar open string amplitudes in the presence of the background NS-NS two-form field. In the decoupling limit of Seiberg and Witten, we find that the nonplanar string amplitudes reproduce the UV/IR mixing of noncommutative field theories. In particular, the investigation of the UV regime of the open string amplitudes shows that certain IR closed string degrees of freedom survive the decoupling limit as previously predicted from the noncommutative field theory analysis. These degrees of freedom are responsible for the quadratic, linear and logarithmic IR singularities when the D-branes embedded in space-time have the codimension zero, one and two, respectively. The analysis is given for both bosonic and supersymmetric open strings.