One-loop Noncommutative U(1) Gauge Theory from Bosonic Worldline Approach

TL;DR

This paper introduces a bosonic worldline approach to compute the one-loop effective action in noncommutative U(1) gauge theory, revealing the emergence of open Wilson lines and connecting to string and matrix theory insights.

Contribution

It develops a novel worldline formalism for noncommutative gauge theories, providing compact expressions for amplitudes and highlighting the role of open Wilson lines as gauge invariants.

Findings

Open Wilson lines appear as gauge invariant completions.

Derived compact expressions for N-point 1PI amplitudes.

Connections made to string theory and matrix theory results.

Abstract

We develop a method to compute the one-loop effective action of noncommutative U(1) gauge theory based on the bosonic worldline formalism, and derive compact expressions for N-point 1PI amplitudes. The method, resembling perturbative string computations, shows that open Wilson lines emerge as a gauge invariant completion of certain terms in the effective action. The terms involving open Wilson lines are of the form reminiscent of closed string exchanges between the states living on the two boundaries of a cylinder. They are also consistent with recent matrix theory analysis and the results from noncommutative scalar field theories with cubic interactions.