title: Information metric from a linear sigma model.
abstract: The idea that a space-time 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 σ models. In this 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 nontrivial solution of the massive Klein-Gordon field (a linear σ model). This realization of the flat space from the simple field theory would be useful to investigate the ideas that relate the space-time geometry with the information geometry.
authors.affiliation: Department of Physics, Rikkyo University, Tokyo 171-8501, Japan.
authors.forename: U
authors.initials: U
authors.lastname: Miyamoto
authors.forename: S
authors.initials: S
authors.lastname: Yahikozawa