On the \(L^{2}\)-metric of vortex moduli spaces
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Publication:632101
DOI10.1016/J.NUCLPHYSB.2010.11.005zbMATH Open1207.81065arXiv1003.1296OpenAlexW2082530314MaRDI QIDQ632101
Author name not available (Why is that?)
Publication date: 14 March 2011
Published in: (Search for Journal in Brave)
Abstract: 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.
Full work available at URL: https://arxiv.org/abs/1003.1296
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