On the L^2-metric of vortex moduli spaces

Details On the L^2-metric of vortex moduli spaces On the L^2-metric of vortex moduli spaces

2010-03-05

arxiv.org/abs/1003.1296v3

Nucl.Phys.B844:308-333,2011

Physics

High Energy Physics

High Energy Physics - Theory

34 pages; v3: typos fixed and reference added

Scientific paper

10.1016/j.nuclphysb.2010.11.005

We derive general expressions for the Kaehler form of the L^2-metric in terms of standard 2-forms on vortex moduli spaces. In the case of abelian vortices in gauged linear sigma-models, this allows us to compute explicitly the Kaehler class of the L^2-metric. As an application we compute the total volume of the moduli space of abelian semi-local vortices. In the strong coupling limit, this then leads to conjectural formulae for the volume of the space of holomorphic maps from a compact Riemann surface to projective space. Finally we show that the localization results of Samols in the abelian Higgs model extend to more general models. These include linear non-abelian vortices and vortices in gauged toric sigma-models.

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