Quantum Aspects of the Noncommutative Sine-Gordon Model

TL;DR

This paper investigates quantum effects in the noncommutative sine-Gordon model, analyzing fluctuations around solitons, computing one-loop functions, and discussing renormalization and noncommutativity corrections.

Contribution

It provides a semi-classical analysis of quantum fluctuations and one-loop corrections in the noncommutative sine-Gordon model, highlighting the spectrum's stability and UV/IR mixing effects.

Findings

Fluctuation spectrum remains similar to the commutative case at O(theta^2)

Logarithmic divergences and UV/IR mixing are present in one-loop functions

Obstacles exist in determining noncommutative corrections to the kink mass

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(theta^2) 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.