Anatomy of Two-Loop Effective Action in Noncommutative Field Theories

TL;DR

This paper calculates the two-loop effective action in noncommutative scalar field theory using worldline methods, revealing its expression through open Wilson lines and connecting to string theory in the Seiberg-Witten limit.

Contribution

It introduces a worldline approach to compute two-loop effective actions in noncommutative field theories, highlighting the role of open Wilson lines and their relation to string theory.

Findings

Two-loop effective action expressed via open Wilson lines.

Connection established between noncommutative field theory and string theory.

Explicit computation of planar and nonplanar contributions.

Abstract

We compute, at two-loop order, one-particle-irreducible Green functions and effective action in noncommutative $\lambda[\Phi^3]_\star$-theory for both planar (g=0, h=3) and nonplanar (g=1, h=1) contributions. We adopt worldline formulation of the Feynman diagrammatics so that relation to string theory diagrammatics is made transparent in the Seiberg-Witten limit. We argue that the resulting two-loop effective action is expressible via open Wilson lines: one-particle-irreducible effective action is generating functional of connected diagrams for interacting open Wilson lines.