Wild nonabelian Hodge theory on curves

Abstract

On a complex curve, we establish a correspondence between integrable connections with irregular singularities, and Higgs bundles such that the Higgs field is meromorphic with poles of any order. The moduli spaces of these objects are obtained by fixing at each singularity the polar part of the connection. We prove that they carry hyperKahler metrics, which are complete when the residue of the connection if semisimple.

More on moduli spaces

References in corpus (4)

• Quasi-Hamiltonian Geometry of Meromorphic Connections
• Stokes Matrices and Poisson Lie Groups
• Nahm Transform For Periodic Monopoles And N=2 Super Yang-Mills Theory
• Hyperkahler Metrics from Periodic Monopoles

Cited by in corpus (13)

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• Wild Quiver Gauge Theories
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• Twisted wild character varieties
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• Quasi BPS Wilson loops, localization of loop equation by homology and exact beta function in the large N limit of SU(N) Yang-Mills theory
• From $S^1$-fixed points to $\mathcal{W}$-algebra representations
• Yang-Mills mass gap, Floer homology, glueball spectrum, and conformal window in large-N QCD
• Asymptotic Geometry of the Moduli Space of Parabolic $SL(2,\mathbb{C})$-Higgs Bundles
• Solving loop equations by Hitchin systems via holography in large-N QCD_4
• Exact beta function from the holographic loop equation of large-N QCD_4
• Twisted spectral correspondence and torus knots
• Twisted local systems solve the (holographic) loop equation of large-N QCD_4