Dubrovin's superpotential as a global spectral curve

TL;DR

This paper demonstrates how spectral curve topological recursion applied to Dubrovin's superpotential can reproduce the associated cohomological field theory, linking integrable systems and algebraic geometry.

Contribution

It establishes a connection between spectral curve topological recursion and Frobenius manifold cohomological field theories for semi-simple points.

Findings

Correlation differentials expansion reproduces cohomological field theory

Application of spectral curve topological recursion to Dubrovin's superpotential

Conditions under which the correspondence holds

Abstract

We apply the spectral curve topological recursion to Dubrovin's universal Landau-Ginzburg superpotential associated to a semi-simple point of any conformal Frobenius manifold. We show that under some conditions the expansion of the correlation differentials reproduces the cohomological field theory associated with the same point of the initial Frobenius manifold.