Opers versus Nonabelian Hodge

For a complex simple simply connected Lie group G, and a compact Riemann surface C, we consider two sorts of families of flat G-connections over C. Each family is determined by a point u of the base of Hitchin’s integrable system for (G, C). One family ∇h̄,u consists of G-opers, and depends on h̄ ∈ C×. The other family ∇R,ζ,u is built from solutions of Hitchin’s equations, and depends on ζ ∈ C×, R ∈ R+. We show that in the scaling limit R → 0, ζ = h̄R, we have ∇R,ζ,u → ∇h̄,u. This establishes and generalizes a conjecture formulated by Gaiotto.