Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 6 (2010), 037, 20 pages      arXiv:0908.1743
Contribution to the Special Issue “Noncommutative Spaces and Fields”

One-Loop Calculations and Detailed Analysis of the Localized Non-Commutative p−2 U(1) Gauge Model

Daniel N. Blaschke a, b, Arnold Rofner a and René I.P. Sedmik a
a) Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstrasse 8-10, A-1040 Vienna, Austria
b) Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria

Received February 10, 2010, in final form April 23, 2010; Published online May 04, 2010

This paper carries forward a series of articles describing our enterprise to construct a gauge equivalent for the θ-deformed non-commutative p−2 model originally introduced by Gurau et al. [Comm. Math. Phys. 287 (2009), 275-290]. It is shown that breaking terms of the form used by Vilar et al. [J. Phys. A: Math. Theor. 43 (2010), 135401, 13 pages] and ourselves [Eur. Phys. J. C: Part. Fields 62 (2009), 433-443] to localize the BRST covariant operator (D2θ2D2)−1 lead to difficulties concerning renormalization. The reason is that this dimensionless operator is invariant with respect to any symmetry of the model, and can be inserted to arbitrary power. In the present article we discuss explicit one-loop calculations, and analyze the mechanism the mentioned problems originate from.

Key words: noncommutative field theory; gauge field theories; renormalization.

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