AGT, Burge pairs and minimal models
We consider the AGT correspondence in the context of the conformal field theory M(p, p')\otimes H, where M(p,p') is the minimal model based on the Virasoro algebra labeled by two co-prime integers p,p' and H is the free boson theory based on the Heisenberg algebra. Using Nekrasov's instanton partition functions without modification to compute conformal blocks in M(p, p')\otimes H leads to ill-defined or incorrect expressions.
We propose the procedure to make this expressions are well defined and check these proposal in two cases: 1. 1-point torus, when the operator insertion is the identity, and 2. The 6-point Ising conforma block on the sphere that involves six Ising magnetic operators.