Eur. Phys. J. C 22, 757-770 (2002)
https://doi.org/10.1007/s100520100829

Anatomy of one-loop effective action in non-commutative scalar field theories

¹ BK21 Physics Research Division & Institute of Basic Science, Sungkyunkwan University, Suwon 440-746 Korea
² School of Physics & Center for Theoretical Physics, Seoul National University, Seoul 151-747 Korea
³ Theory Division, CERN, 1211 Genève, Switzerland

Received: 22 July 2001
Revised: 19 October 2001
Published online: 7 December 2001

Abstract

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