Information metric from a linear sigma model

The idea that a spacetime metric emerges as a Fisher-Rao `information metric' of instanton moduli space has been examined in several field theories such as the Yang-Mills theories and nonlinear sigma models. In this brief paper, we report that the flat Euclidean or Minkowskian metric, rather than an anti-de Sitter metric that generically emerges from instanton moduli spaces, can be obtained as the Fisher-Rao metric from a non-trivial solution of the massive Klein-Gordon field (a linear sigma model). This realization of the flat space from the simple field theory would be useful to investigate the ideas that relate the spacetime geometry with the information geometry.