Asymptotic behaviour of large-scale solutions of Hitchin's equations in higher rank

Abstract

Let X be a compact Riemann surface. Let (E, θ) be a stable Higgs bundle of degree 0 on X. Let h det(E) denote a flat metric of the determinant bundle det(E). For any t > 0, there exists a unique harmonic metric ht of (E, θ) such that det(ht) = h det(E) . We prove that if the Higgs bundle is induced by a line bundle on the normalization of the spectral curve, then the sequence ht is convergent to the naturally defined decoupled harmonic metric at the speed of the exponential order. We also obtain a uniform convergence for such a family of Higgs bundles.