On the Riemannian geometry of Seiberg-Witten moduli spaces

JOURNAL OF GEOMETRY AND PHYSICS

卷:58

Article

Becker, Christian

关键词: Seiberg-Witten theory;    Moduli spaces;    Gauge theory;    L-2 metrics;   

DOI  :  10.1016/j.geomphys.2008.05.005

来源: Elsevier

【 摘 要 】

We construct a natural L-2-metric on the perturbed Seiberg-Witten moduli spaces m(mu)+ of a compact 4-manifold M, and we study the resulting Riemannian geometry of m(mu)+. We derive a formula which expresses the sectional curvature of m(mu)+ in terms of the Green operators of the deformation complex of the Seiberg-Witten equations. In case M is simply connected, we construct a Riemannian metric on the Seiberg-Witten principal U(1) bundle n -> m(mu)+ such that the bundle projection becomes a Riemannian submersion. On a Kahler surface M, the L-2-metric on m(mu)+ coincides with the natural Kahler metric on moduli spaces of vortices. (C) 2008 Elsevier B.V. All rights reserved.

【 授权许可】

Free