TL;DR
This paper analyzes the two-dimensional sine-Gordon model across different regimes, revealing its asymptotic freedom in both infrared and ultraviolet limits through renormalization group methods.
Contribution
It provides a detailed renormalization group analysis of the sine-Gordon model in two regimes, highlighting its asymptotic freedom properties.
Findings
Model is asymptotically free in the infrared for beta > 8 pi.
Model is asymptotically free in the ultraviolet for beta < 8 pi.
Different cutoff schemes reveal consistent asymptotic behaviors.
Abstract
We study the sine-Gordon model in two dimensional space time in two different domains. For beta > 8 pi and weak coupling, we introduce an ultraviolet cutoff and study the infrared behavior. A renormalization group analysis shows that the model is asymptotically free in the infrared. For beta < 8 pi and weak coupling, we introduce an infrared cutoff and study the ultraviolet behavior. A renormalization group analysis shows that the model is asymptotically free in the ultraviolet.
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