Toda 3-Point Functions From Topological Strings II

TL;DR

This paper connects Toda 3-point functions to topological string theory, deriving known formulas through Higgsing of $T_N$ theories, expanding the understanding of the AGT-W correspondence.

Contribution

It demonstrates how semi-degeneration in Toda theory corresponds to Higgsing in $T_N$ theories, providing a new derivation of Fateev and Litvinov's formula.

Findings

Derived Toda 3-point functions from topological strings.

Linked semi-degeneration to Higgsing in $T_N$ theories.

Reproduced Fateev and Litvinov's formula.

Abstract

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.