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 co-prime 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 ill-defined 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 σ-column of , we obtain a well-defined expression that we identify with . We check the correctness of this expression for 1. Any 1-point on the torus, when the operator insertion is the identity, and 2. The 6-point on the sphere that involves six Ising magnetic operators.
- Publication:
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Journal of High Energy Physics
- Pub Date:
- June 2014
- DOI:
- 10.1007/JHEP06(2014)177
- arXiv:
- arXiv:1404.7075
- Bibcode:
- 2014JHEP...06..177B
- Keywords:
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- Supersymmetric gauge theory;
- Conformal and W Symmetry;
- High Energy Physics - Theory
- E-Print:
- 22 pages. Simplified the presentation