Topological Field Theory and Superfluid Thin Film

目前的研究表明，二维Abelian Higgs模型在某些参数区域成为拓扑场论，而在另一些参数区域又包含XY模型，是研究超流薄膜的有效理论。近年来，我们用重整化群方法研究了Abel Higgs模型，阐明了该模型的整体结构，特别是拓扑激发和自旋波的行为。为此，至关重要的是要找出阿贝尔希格斯模型等价于大质量sine-Gordon模型的事实。然后用重整化群方法研究了有质量的sine-Gordon模型，在通常的动量截断下，用数值方法得到了递推方程的解。结果表明，重整化群有两条不动线。作为今年获得的另一个结果，我们证明了阿贝尔Higgs模型等价于具有四费米相互作用的二维QED。从阿贝尔希格斯模型的知识，这个理论的真空结构澄清和关联函数明确计算。

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.