Spectral curves for Gromov-Witten theories

We show that under certain conditions Dubrovin's superpotential for a conformal Frobenius manifold at a semisimple point provides a global spectral curve for the associated Gromov-Witten theory (cohomological field theory, in general). This means that the correlators of this cohomological field theory are reproduced by the spectral curve topological recursion procedure on this curve.
Based on P.Dunin-Barkowski,P.Norbury,N.Orantin,A.Popolitov,S.Shadrin "Dubrovin's superpotential as a global spectral curve", http://arxiv.org/abs/1509.06954 [4] .