Instantons, the Information Metric, and the AdS/CFT Correspondence

Abstract

We describe some remarkable properties of the so-called Information Metric on instanton moduli space. This Metric is manifestly gauge and conformally invariant and coincides with the Euclidean AdS_5 metric on the one-instanton SU(2) moduli space for the standard metric on R^4. We propose that for an arbitrary boundary metric the AdS/CFT bulk space-time is the instanton moduli space equipped with the Information Metric. To test this proposal, we examine the variation of the instanton moduli and the Information Metric for first-order perturbations of the boundary metric and obtain three non-trivial and somewhat surprising results: (1) The perturbed Information Metric is Einstein. (2) The perturbed instanton density is the corresponding massless boundary-to-bulk scalar propagator. (3) The regularized boundary-to-bulk geodesic distance is proportional to the logarithm of the perturbed instanton density. The Hamilton-Jacobi equation implied by (3) equips the moduli space with a rich geometrical structure which we explore. These results tentatively suggest a picture in which the one-instanton sector of SU(2) Yang-Mills theory (rather than some large-N limit) is in some sense holographically dual to bulk gravity.

arXiv comment44 pages, LaTeX, no figures

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Cited by in corpus (9)

• U(N) Instantons on N=1/2 superspace -- exact solution & geometry of moduli space
• 5d Black Hole as Emergent Geometry of Weakly Interacting 4d Hot Yang-Mills Gas
• Non-Commutative Instantons and the Information Metric
• Information Metric on Instanton Moduli Spaces in Nonlinear Sigma Models
• The Information Metric on the moduli space of instantons with global symmetries
• Statistical Inference and String Theory
• Information metric from a linear sigma model
• Introduction to Gauge/Gravity Duality (TASI Lectures 2017)
• Probability Density Functions from the Fisher Information Metric