Information Metric on Instanton Moduli Spaces in Nonlinear Sigma Models

Abstract

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.

9 pages, LaTeX; added references for section 1; typos added

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• The Information Metric on the moduli space of instantons with global symmetries
• Information metric from a linear sigma model
• Metric on a Statistical Space-Time