The universal connection and metrics on moduli spaces (Q2385984)

This article deals with metrics in gauge theoretic moduli spaces. Using the universal matrices which appear in the universal connection introduced by \textit{M. S. Narasimhan} and \textit{S. Ramanan} [Am. J. Math. 83, 563--572 (1961; Zbl 0114.38203)], the authors give a class of the metrics. Succeeding the natural properties of the matrices, the metrics naturally behave, for example, in the instanton moduli spaces. The authors explicitly construct the metrics on the \(c_2=1\), SU(2) moduli space of instantons on \(\mathbb R^4\) for various universal matrices based upon the ADHM construction [\textit{M. F. Atiyah, N. J. Hitchin, V. G. Drinfeld} and \textit{Yu. I. Manin}, Phys. Lett. A 65, 185--187 (1978; Zbl 0424.14004)].