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

Abstract

In this note we revisit Hitchin's prescription \cite{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 ${\mathbb{CP}}^N$ sigma model on ${\mathbb{R}}^2$.

5 pages, no figures, sorry

References in corpus (2)

• Gravity Dual of Quantum Information Metric
• Tomography from Entanglement

Cited by in corpus (5)

• Information geometry in quantum field theory: lessons from simple examples
• Towards complexity of primary-deformed Virasoro circuits
• Introduction to Gauge/Gravity Duality (TASI Lectures 2017)
• Holographic Fisher Information Metric in Schrödinger Spacetime
• Hessian potential for Fefferman-Graham metric