Toda 3-Point Functions From Topological Strings II

In arXiv:1409.6313 we proposed a formula for the 3-point structure constants of Toda field theory, derived using topological strings and the AGT-W correspondence from the partition functions of the non-Lagrangian $T_N$ theories on $S^4$. In this article, we show how the semi-degeneration of one of the three primary fields on the Toda side corresponds to a particular Higgsing of the $T_N$ theories and derive the well-known formula by Fateev and Litvinov.