S-duality in hyperkaehler Hodge theory

Abstract

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.

Dedicated to Nigel Hitchin on the occasion of his sixtieth birthday

References in corpus (7)

• Dyon - Monopole Bound States, Self-Dual Harmonic Forms on the Multi-Monopole Moduli Space, and SL(2,Z) Invariance in String Theory
• Mirror symmetry, Langlands duality, and the Hitchin system
• The Moduli Space Metric for Well Separated BPS Monoples
• Moduli Spaces of Parabolic Higgs Bundles and Parabolic K(D) Pairs over Smooth Curves: I
• Betti numbers of holomorphic symplectic quotients via arithmetic Fourier transform
• Examples of mirror partners arising from integrable systems
• $O(-2)$ Blow-up Formula via Instanton Calculus on $\widehat{C^2/Z_2}$ and Weil Conjecture

Cited by in corpus (1)

• Mixed Hodge polynomials of character varieties