Equal-mass sunset integrals and genus-zero local Gromov--Witten theory of Calabi--Yau $n$-folds

We prove an exact identity, as convergent logarithmic germs at large Euclidean momentum, between the equal-mass two-dimensional $(n-1)$-loop sunset Feynman integral, with $n\geq4$, and the genus-zero one-point descendant invariants of the local Calabi--Yau $n$-fold $X_n=\operatorname{Tot}(K_{F_n})$,