Comments on Noncommutative Perturbative Dynamics

TL;DR

This paper investigates IR singularities in noncommutative field theories, proposing they originate from exchanges of new light degrees of freedom akin to closed string interactions, with complex two-loop IR behaviors.

Contribution

It introduces a novel interpretation of IR singularities as exchanges of light degrees of freedom, linking noncommutative field theory phenomena to string theory concepts.

Findings

IR singularities linked to light degrees of freedom

Propagators suggest extra-dimensional interpretation

Complex two-loop IR behavior observed

Abstract

We analyze further the IR singularities that appear in noncommutative field theories on R^d. We argue that all IR singularities in nonplanar one loop diagrams may be interpreted as arising from the tree level exchanges of new light degrees of freedom, one coupling to each relevant operator. These exchanges are reminiscent of closed string exchanges in the double twist diagrams in open string theory. Some of these degrees of freedom are required to have propagators that are inverse linear or logarithmic. We suggest that these can be interpreted as free propagators in one or two extra dimensions respectively. We also calculate some of the IR singular terms appearing at two loops in noncommutative scalar field theories and find a complicated momentum dependence which is more difficult to interpret.