Anatomy of One-Loop Effective Action in Noncommutative Scalar Field Theories

TL;DR

This paper computes the one-loop effective action for noncommutative scalar fields with cubic interactions, demonstrating agreement with string theory results and revealing a simplified form involving scalar open Wilson lines in certain limits.

Contribution

It provides explicit calculations of planar and nonplanar contributions using worldline formulation and shows the resummation into Wilson line operators at low energy and large noncommutativity.

Findings

Agreement with string worldsheet computations

Simplification of nonplanar part into Wilson line operators

Resummation into a quadratic action in specific limits

Abstract

One-loop effective action of noncommutative scalar field theory with cubic self-interaction is studied. Utilizing worldline formulation, both planar and nonplanar part of the effective action are computed explicitly. We find complete agreement of the result with Seiberg-Witten limit of string worldsheet computation and standard Feynman diagrammatics. We prove that, at low-energy and large noncommutativity limit, nonplanar part of the effective action is simplified enormously and is resummable into a quadratic action of scalar open Wilson line operators.