Anatomy of One-Loop Effective Action in Noncommutative Scalar Field Theories

Abstract

One-loop effective action of noncommutative scalar field theory with cubic self-interaction is studied. Utilizing worldline formulation, both planar and nonplanar part of the effective action are computed explicitly. We find complete agreement of the result with Seiberg-Witten limit of string worldsheet computation and standard Feynman diagrammatics. We prove that, at low-energy and large noncommutativity limit, nonplanar part of the effective action is simplified enormously and is resummable into a quadratic action of scalar open Wilson line operators.

26 pages, Latex, 4 eps figures, v2. typos corrected, v3. combinatorics corrected

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