Gross–Siebert central-fiber and large-complex-limit conjecture for Hitchin moduli spaces

Consider the Gross–Siebert toric degeneration of Hitchin's moduli spaces and the large complex degeneration of the same moduli space. The central fiber of the first is the special fiber produced by the Gross–Siebert construction, while the large complex limit point is the limiting point of the large complex degeneration. Gross–Siebert central-fiber conjecture. The central fiber of the Gross–Siebert toric degeneration of Hitchin's moduli spaces coincides with the large complex limit point for the large complex degeneration of Hitchin's moduli space. The conjecture proposes a precise compatibility between the algebraic toric degeneration and the large-complex-structure limit; the paper gives no resolution.