Gaiotto–Moore–Neitzke metric identification conjecture for Hitchin moduli spaces

Let $\mathcal{M}$ be an $SU(2)$ Hitchin moduli space with only regular singularities and regular semisimple residues, equipped with the hyperkähler metric constructed from Fock–Goncharov coordinates via the twistor construction. Let $g_{\mathrm{Hitchin}}$ denote Hitchin's hyperkähler quotient metric. Metric identification conjecture. The hyperkähler metric constructed above is isometric to $g_{\mathrm{Hitchin}}$. This conjecture asserts that the Gaiotto–Moore–Neitzke twistor construction recovers the original hyperkähler quotient metric on Hitchin's moduli space; the source gives no resolution of the conjecture.