非线性西格玛模型中瞬时模空间上的信息度量
Information Metric on Instanton Moduli Spaces in Nonlinear Sigma Models
摘要：
研究二维非线性西格玛模型中瞬子模空间上的信息度量。在CP ^1模型中，拓扑荷Q=k的一个瞬子的模空间上的信息度量是一个三维双曲度量，对应于三维欧氏反德西特时空度量，信息度量的总尺度因子是（4k^2）/3;这意味着截面曲率是-3/（4k^2）。我们还计算了CP^2模型中的信息度量。
英文摘要：
We study the information metric on instanton moduli spaces in two-dimensional nonlinear sigma models. In the CP^1 model, the information metric on the moduli space of one instanton with the topological charge Q=k which is any positive integer is a three-dimensional hyperbolic metric, which corresponds to Euclidean anti--de Sitter space-time metric in three dimensions, and the overall scale factor of the information metric is (4k^2)/3; this means that the sectional curvature is -3/(4k^2). We also calculate the information metric in the CP^2 model.
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