Integrable models through tt∗ equations

In this short Letter we investigate the integrability of some N=2 superconformal field theories (SCFT) deformed by massive (relevant) operators. They have Landau-Ginzburg (LG) description and classified into A, D, and E by singularity theory. We focus on Dn+1 and E6,8 cases with particular deformations for each model. They are already known to be integrable by the existence of solutions of generalized Yang-Baxter equation (graph-Yang-Baxter). We study the same models with different approach: we find topological-antitopological (tt∗) equation that is the equation satisfied by the ground state metric (analogue of Zamolodchikov metric). The tt∗ equations thus obtained turns out to be Toda equations as a function of perturbation parameter.