Information metric from a linear sigma model

TL;DR

This paper demonstrates that the Fisher-Rao information metric derived from a linear sigma model's solutions can reproduce flat spacetime geometry, offering insights into the connection between information geometry and spacetime structure.

Contribution

It shows that flat spacetime metrics can be obtained from a linear sigma model's solutions, contrasting with previous results that yielded anti-de Sitter metrics from instanton moduli spaces.

Findings

Flat space metric derived from a linear sigma model.

Contrasts with anti-de Sitter metrics from instanton moduli.

Provides a simple field theory example linking geometry and information.

Abstract

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.