TL;DR
This paper explores the connection between 4d N=2 gauge theories with quiver tails and 2d Toda CFT, focusing on how Coulomb-branch parameters relate to Toda states and their three-point functions.
Contribution
It introduces a new identification of Toda CFT states corresponding to Coulomb-branch parameters in linear quiver gauge theories with varying ranks.
Findings
Established a correspondence between Coulomb-branch parameters and Toda states.
Analyzed three-point functions and descendants in the context of quiver tails.
Extended the AGT relation to theories with gauge groups of different ranks.
Abstract
The relation between the partition function of N=2 gauge theories in 4d and conformal Toda field theory in 2d is explained for the case where the 4d theory is a linear quiver with "quiver tails". That is when the 4d theory has gauge groups of different rank. We propose an identification of a subset of the states of Toda CFT which represent the Coulomb-branch parameters of the different rank gauge multiplets and study their three-point functions and descendants.
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