Noncommutative Perturbative Dynamics

TL;DR

This paper investigates the perturbative behavior of noncommutative field theories, revealing a unique UV/IR mixing where high-energy virtual particles cause low-momentum singularities, affecting the effective action.

Contribution

It provides a detailed analysis of UV/IR mixing in noncommutative field theories and interprets divergences as IR effects arising from noncommutativity.

Findings

UV/IR mixing causes low-momentum singularities.

Nonplanar diagrams exhibit IR divergences.

The phenomenon parallels open string theory duality.

Abstract

We study the perturbative dynamics of noncommutative field theories on R^d, and find an intriguing mixing of the UV and the IR. High energies of virtual particles in loops produce non-analyticity at low momentum. Consequently, the low energy effective action is singular at zero momentum even when the original noncommutative field theory is massive. Some of the nonplanar diagrams of these theories are divergent, but we interpret these divergences as IR divergences and deal with them accordingly. We explain how this UV/IR mixing arises from the underlying noncommutativity. This phenomenon is reminiscent of the channel duality of the double twist diagram in open string theory.