AGT, Burge pairs and minimal models
Abstract
We consider the AGT correspondence in the context of the conformal field theory , where is the minimal model based on the Virasoro algebra labeled by two coprime integers { p, p'}, 1 < p < p', and is the free boson theory based on the Heisenberg algebra . Using Nekrasov's instanton partition functions without modification to compute conformal blocks in leads to illdefined or incorrect expressions. Let be a conformal block in , with n consecutive channels χ _{ ι }, _{ ι } n, and let χ _{ ι } carry states from , where is an irreducible highest weight representation, labeled by two integers { r _{ ι } , s _{ ι }}, 0 < r _{ ι } < p, 0 < s _{ ι } < p', and is the Fock space of . We show that restricting the states that flow in χ_{ ι }, ι = 1 , · · · , n, to states labeled by partition pairs that satisfy , and ,where is the σcolumn of , we obtain a welldefined expression that we identify with . We check the correctness of this expression for 1. Any 1point on the torus, when the operator insertion is the identity, and 2. The 6point on the sphere that involves six Ising magnetic operators.
 Publication:

Journal of High Energy Physics
 Pub Date:
 June 2014
 DOI:
 10.1007/JHEP06(2014)177
 arXiv:
 arXiv:1404.7075
 Bibcode:
 2014JHEP...06..177B
 Keywords:

 Supersymmetric gauge theory;
 Conformal and W Symmetry;
 High Energy Physics  Theory
 EPrint:
 22 pages. Simplified the presentation