Instantons and the information metric
| dc.creator | Groisser, David | |
| dc.creator | Murray, Michael K. | |
| dc.date | 1996-11-25 | |
| dc.date.accessioned | 2026-07-07T09:12:55Z | |
| dc.date.available | 2026-07-07T09:12:55Z | |
| dc.description | 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 $L^2$ 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 $S^4$ 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 $\C P_2$. | |
| dc.description | 18 pages, Latex | |
| dc.identifier | https://arxiv.org/abs/dg-ga/9611008 | |
| dc.identifier | http://arxiv.org/abs/dg-ga/9611008 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152185 | |
| dc.subject | Differential Geometry | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Instantons and the information metric | |
| dc.type | text |