Abstract. In this paper, we first use semi-classical methods to study quantum field theoretical aspects of the integrable noncommutative sine-Gordon model proposed in [hep-th/0406065]. In particular, we examine the fluctuations at quadratic order around the static kink solution using the background field method. We derive equations of motion for the fluctuations and argue that at O(θ²) the spectrum of fluctuations remains essentially the same as that of the corresponding commutative theory. We compute the one-loop two-point functions of the sine-Gordon field and the additional scalar field present in the model and exhibit logarithmic divergences, only some of which lead to UV/IR mixing. We briefly discuss the one-loop renormalization in Euclidean signature and comment on the obstacles in determining the noncommutativity corrections to the quantum mass of the kink.

Key words: Solitons Monopoles and Instantons; Non-Commutative Geometry; Integrable Field Theories

E-print number: 0708.1310
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Received 15 August 2007, accepted for publication 16 August 2007
Published 3 September 2007