Ooguri–Vafa local model conjecture for singular Hitchin fibers

Let $\bar{\mathcal{M}}^{0}=\mathcal{M}^{0}/Q$ be the SYZ mirror of the local model, and let $\Omega(\xi)$ be the holomorphic symplectic form of its hyperkähler metric. Let $u_0$ be the singular-fiber point, and let $\Omega^{OV}(\xi)$ be the holomorphic symplectic form of the Ooguri–Vafa space with

$$\Omega_1=\Omega_{-1}=2,\qquad \Omega_q=0\quad q\neq\pm1.$$

Ooguri–Vafa local model conjecture. As $R\to\infty$, in a sufficiently small tubular neighborhood of the singular fiber over $u_0$,

$$\Omega(\xi)=\Omega^{OV}+O(c_1Re^{-c_2R}),$$

where $c_1,c_2$ depend on the choice of neighborhood and $c_2>0$. This predicts that the Ooguri–Vafa space gives the leading local metric model near a singular Hitchin fiber; the source gives no resolution.