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 CP1 model, the information metric on the moduli space of one instanton with the topological charge Q=k(k > or =1) 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 CP2 model.