Noncommutative Field Theory from String Theory: Two-loop Analysis

TL;DR

This paper demonstrates that noncommutative  field theory's two-loop UV/IR mixing can be derived from string theory with background fields, extending previous one-loop insights and generalizing to complex world-sheet topologies.

Contribution

It provides a two-loop analysis connecting noncommutative field theory and string theory, extending the stretched string picture to higher genus surfaces.

Findings

Matching amplitudes between string theory and noncommutative field theory.

Generalization of the stretched string picture to two-loop amplitudes.

Framework for incorporating closed and open string insertions at higher genus.

Abstract

Noncommutative \phi^3 field theory in six dimensions exhibits the logarithmic UV/IR mixing at the two-loop order. We show that open string theory in the presence of constant background NS-NS two-form field yields the same amplitude upon taking a decoupling limit. The stretched string picture proposed on the basis of one-loop analysis naturally generalizes to the two-loop amplitudes in consideration. Our string theory formulation can incorporate the closed string insertions as well as open string insertions. Furthermore, the analysis of the world-sheet partition function and propagators can be straightforwardly generalized to Riemann surfaces with genus zero but with an arbitrary number of boundaries.