Author:
Lara R. I. García,Speight J. M.
Abstract
AbstractIt is proved that the normalized$$L^2$$L2metric on the moduli space ofn-vortices on a two-sphere, endowed with any Riemannian metric, converges uniformly in the Bradlow limit to the Fubini–Study metric. This establishes, in a rigorous setting, a longstanding informal conjecture of Baptista and Manton.
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Statistical and Nonlinear Physics
Reference17 articles.
1. Aubin, T.: Nonlinear Analysis on Manifolds. Monge–Ampère Equations, Vol. 252 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, New York (1982)
2. Bando, S., Urakawa, H.: Generic properties of the eigenvalue of the Laplacian for compact Riemannian manifolds. Tohoku Math. J. 35, 155–172 (1983)
3. Baptista, J.M.: On the L$$^{2}$$-metric of vortex moduli spaces. Nucl. Phys. B 844, 308–333 (2011)
4. Baptista, J.M., Manton, N.S.: The dynamics of vortices on $$S^2$$ near the Bradlow limit. J. Math. Phys. 44, 3495–3508 (2003)
5. Berger, M., Gauduchon, P., Mazet, E.: Le Spectre d’une Variété Riemannienne. Lecture Notes in Mathematics, vol. 194. Springer-Verlag, Berlin-New York (1971)