Convergence of anti-self-dual connections on \(SU(n)\)-bundles over product of two Riemann surfaces
The main object of this article is to investigate the asymptotic behaviour of the anti-self-dual Yang-Mills equations on a \(SU(n)\) bundle of two compact Riemann surfaces, establishing a convergence result in the adiabatic limit. The author points out that ``the phenomenon for the Yang-Mills instantons we are encountering here bears a strong analogy with the behaviour of harmonic mappings from Riemannian surfaces with uniformly bounded total energy.'' \dots{}He claims that ``\(C^0\)-convergence is important to study the topology of the moduli spaces.''\dots{} ``As for non-minimizing critical points of the Yang-Mills functional over a product of two compact surfaces''\dots{} ``our method should imply convergence to a harmonic map instead of a holomorphic one.'' For the geometry of anti-self-dual connections and the Kuranishi map, see [\textit{M. Itoh}, J. Math. Soc., Japan 40, 9-33 (1988; Zbl 0619.53042)]; the module of anti-self-dual connections and the Kuranishi map, see [\textit{M. Itoh}, Proc. Japan Acad., Ser. A 57, 176-180 (1981; Zbl 0493.58018)]; explicit constructions of Yang-Mills instantons [\textit{M. Bianchi, F. Fucito, G. Rossi}, and \textit{M. Martellini}, Nucl. Phys. B 473, 367-404 (1996; Zbl 0925.53009)].
scientific article; zbMATH DE number 1294595