Anatomy of two-loop effective action in noncommutative field theories

Abstract

We compute, at two-loop order, one-particle-irreducible Green functions and effective action in noncommutative λ[ Φ 3] ★-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.