Abstract
We present a renormalization group analysis for the hyperbolic sine-Gordon (sinh-Gordon) model in two dimensions. We derive the renormalization group equations based on the dimensional regularization method and the Wilson method. The same equations are obtained using both these methods. We have two parameters $\alpha$ and $\beta\equiv \sqrt{t}$ where $\alpha$ indicates the strength of interaction of a real salar field and $t=\beta^2$ is related with the normalization of the action. We show that $\alpha$ is renormalized to zero in the high-energy region, that is, the sinh-Gordon theory is an asymptotically free theory. We also show a non-renormalization property that the beta function of $t$ vanishes in two dimensions.
Highlights
The sinh-Gordon model has been studied as a field theory model[20–26]. It appears that the sinh-Godron model is similar to the φ4 model when we expand cosh φ in terms of φ
We have presented a renormalization group analysis of the sinh-Gordon model
The analysis is based on the dimensional regularization method and the Wilson renormalization group method
Summary
The sine-Gordon model is an important model and plays a significant role in physics[1–14]. The sinh-Gordon model has been studied as a field theory model[20–26]. It appears that the sinh-Godron model is similar to the φ4 model when we expand cosh φ in terms of φ. Both models have a kink solution as a classical solution. In this paper we investigate the sinh-Gordon model by using the renormalization group theory. 3, we derive renormalization group equations on the basis of the dimensional regularization method. 4, we examine the renormalization procedure based on the Wilson method, and in Sect. 6 we consider the generalized model with high-frequency modes and examine their effect on scaling property.
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