S-duality in hyperkaehler Hodge theory

Details S-duality in hyperkaehler Hodge theory S-duality in hyperkaehler Hodge theory

2007-09-04

arxiv.org/abs/0709.0504v1

Mathematics

Algebraic Geometry

Dedicated to Nigel Hitchin on the occasion of his sixtieth birthday

Scientific paper

Here we survey questions and results on the Hodge theory of hyperkaehler quotients, motivated by certain S-duality considerations in string theory. The problems include L^2 harmonic forms, Betti numbers and mixed Hodge structures on the moduli spaces of Yang-Mills instantons on ALE gravitational instantons, magnetic monopoles on R^3 and Higgs bundles on a Riemann surface. Several of these spaces and their hyperkaehler metrics were constructed by Nigel Hitchin and his collaborators.

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