On the L^2-metric of vortex moduli spaces

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.

34 pages; v3: typos fixed and reference added

References in corpus (7)

• Manifestly Supersymmetric Effective Lagrangians on BPS Solitons
• Statistical Mechanics of Vortices from D-branes and T-duality
• One-vortex moduli space and Ricci flow
• The Moduli Space Metric for Well-Separated Non-Abelian Vortices
• Vortex invariants and toric manifolds
• Twisting gauged non-linear sigma-models
• The volume of the space of holomorphic maps from S^2 to CP^k

Cited by in corpus (3)

• Fractional and semi-local non-Abelian Chern-Simons vortices
• Group Theory of Non-Abelian Vortices
• The volume of the space of holomorphic maps from S^2 to CP^k