Conformal blocks of W_N Minimal Models and AGT correspondence

TL;DR

This paper explores the AGT correspondence in W_N minimal models, proposing modifications to the conformal blocks representation based on integrable structures and orthogonal basis reductions, resulting in a combinatorial formula involving Young diagrams.

Contribution

It introduces a modified AGT representation for W_N minimal models' conformal blocks, connecting integrable structures with combinatorial methods.

Findings

Derived explicit combinatorial formulas for minimal model conformal blocks.

Linked orthogonal basis reduction to the AGT correspondence.

Provided a sum-over-Young-diagrams representation with restrictions.

Abstract

We study the AGT correspondence between four-dimensional supersymmetric gauge field theory and two-dimensional conformal field theories in the context of W_N minimal models. The origin of the AGT correspondence is in a special integrable structure which appears in the properly extended conformal theory. One of the basic manifestations of this integrability is the special orthogonal basis which arises in the extended theory. We propose modification of the AGT representation for the W_N conformal blocks in the minimal models. The necessary modification is related to the reduction of the orthogonal basis. This leads to the explicit combinatorial representation for the conformal blocks of minimal models and employs the sum over N-tupels of Young diagrams with additional restrictions.