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 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. (C) 2002 Elsevier Science B.V. All rights reserved.