Compatibility of Goldman's symplectic form with the complex structure on the $\mathrm{S}\mathrm{L}(3,\mathbb{R})$ Hitchin component

We prove that, on the $\mathrm{S}\mathrm{L}(3,\mathbb{R})$ Hitchin component, the Goldman symplectic form and the Labourie-Loftin complex structure are compatible and together determine a (mapping class group invariant) pseudo-Kähler structure.