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.

27 pages, Latex, 6 figures using pictex, v2. typos corrected

References in corpus (4)

• Open Wilson Lines and Generalized Star Product in Noncommutative Scalar Field Theories
• Anatomy of One-Loop Effective Action in Noncommutative Scalar Field Theories
• Interacting Open Wilson Lines in Noncommutative Field Theories
• UV/IR connection, a matrix perspective

Cited by in corpus (7)

• A non-perturbative study of 4d U(1) non-commutative gauge theory -- the fate of one-loop instability
• U(N) Instantons on N=1/2 superspace -- exact solution & geometry of moduli space
• From UV/IR mixing to closed strings
• UV-IR mixing and the quantum consistency of noncommutative gauge theories
• Bound-state gravity from higher derivatives
• Strings, Dipoles and Fuzzy Spheres
• Softer Hard Scattering and Noncommutative Gauge-String Duality