The Information Metric on the moduli space of instantons with global symmetries

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In this note we revisit Hitchin's prescription Hitchin of the Fisher metric as a natural measure on the moduli space of instantons that encodes the space-time symmetries of a classical field theory. Motivated by the idea of the moduli space of supersymmetric instantons as an emergent space in the sense of the gauge/gravity duality, we extend the prescription to encode also global symmetries of the underlying theory. We exemplify our construction with the instanton solution of the CPⁿ sigma model on R².