Topological Field Theory and Superfluid Thin Film

点击翻译按钮获取中文摘要

Present study showed that the 2-dimensional Abelian Higgs model becomes a topological field theory at some parameter region, and also it containes the XY model at another parameter region, which is an effective theory for superfluid thin film. In the present year, we studied the Abelian Higgs model by a method of the renormalization group, and clarified the global structure of this model, especially the behavior of the topological exciations and the spin wave. To this end, it was crucial to find out the fact that the Abelian Higgs model is equivalent to the massive sine-Gordon model. Then the massive sine-Gordon model was studied by the renormalization-group method with the usual momentum cut off, and solutions to the recursion equations were obtained by numerical method. The solutions show that there are two fixed line of the renormalization group. One corresponds to low-temperature phase of the XY model and the other is the topological-field phase.As another result obtained this year, we proved that the Abelian Higgs model is equivalent to the 2-dimensional QED with the four-fermi interaction. From the knowledge of the Abelian Higgs model, the vacuum structure of this theory was clarified and correlation functions were explicitly calculated.