Convergence of anti-self-dual connections on \(SU(n)\)-bundles over product of two Riemann surfaces
type: Item
instance of: scholarly article
title: Convergence of anti-self-dual connections on \(SU(n)\)-bundles over product of two Riemann surfaces
zbMATH Open document ID: 0945.53017
published in: Communications in Mathematical Physics
publication date: 2000-09-20T00:00:00Z
review text: 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)].
reviewed by: L. Del Riego
Mathematics Subject Classification ID: 53C07
Mathematics Subject Classification ID: 58E15
zbMATH DE Number: 1294595
zbMATH Keywords: anti-self-dual connection
zbMATH Keywords: moduli space
zbMATH Keywords: Riemann surface
zbMATH Keywords: \(SU(n)\) bundle
zbMATH Keywords: Yang-Mills instanton
author: Jingyi Chen
MaRDI profile type: Publication
full work available at URL: s002200050436
OpenAlex ID: W2085818259
Wikidata QID: Q125577938
DOI: 10.1007/S002200050436
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description: scientific article; zbMATH DE number 1294595