1996/11/25 by David Groisser, Michael K. Murray, Groisser, David +1 · 1 citation
Chemistry · Computer Science · Social Sciences · #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #History and advancements in chemistry #Intelligence, Security, War Strategy #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.dg-ga/9611008
openalex publication_date 1996/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The information metric arises in statistics as a natural inner product on a space of probability distributions. In general this inner product is positive semi-definite but is potentially degenerate. By associating to an instanton its energy density, we can examine the information metric \bf g on the moduli spaces \M of self-dual connections over Riemannian 4-manifolds. Compared with the more widely known L2 metric, the information metric better reflects the conformal invariance of the self-dual Yang-Mills equations, and seems to have better completeness properties. In the case of SU(2) instantons on S4 of charge one, \bf g is known to be the hyperbolic metric on the five-ball. We show more generally that for charge-one SU(2) instantons over 1-connected, positive-definite manifolds, \bf g is nondegenerate and complete in the collar region of \M, and is `asymptotically hyperbolic' there; \bf g vanishes at the cone points of \M. We give explicit formulae for the metric on the space of instantons of charge one on \C P2.