Conformal blocks of W_N Minimal Models and AGT correspondence

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.

arXiv comment16 pages; v2: typos removed, more comments, references added; v3: minor corrections, references added, JHEP version

References in corpus (13)

• Liouville Correlation Functions from Four-dimensional Gauge Theories
• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• On AGT relation in the case of U(3)
• On combinatorial expansion of the conformal blocks arising from AGT conjecture
• The Power of Nekrasov Functions
• Super Liouville conformal blocks from N=2 SU(2) quiver gauge theories
• Higher Equations of Motion in Liouville Field Theory
• Integrable structure, W-symmetry and AGT relation
• Correlation Functions in Holographic Minimal Models
• Conformal blocks in Virasoro and W theories: duality and the Calogero-Sutherland model
• Null vectors of the W_3 algebra
• Generalized Jack polynomials and the AGT relations for the $SU(3)$ group
• Correlators in W_N Minimal Model Revisited

Cited by in corpus (21)

• Monodromic vs geodesic computation of Virasoro classical conformal blocks
• Classical conformal blocks via AdS/CFT correspondence
• Virasoro vacuum block at next-to-leading order in the heavy-light limit
• A slow review of the AGT correspondence
• Wilson Loops and Chiral Correlators on Squashed Sphere
• SH${}^c$ Realization of Minimal Model CFT: Triality, Poset and Burge Condition
• AGT, N-Burge partitions and W_N minimal models
• Holomorphic field realization of SH${}^c$ and quantum geometry of quiver gauge theories
• Quantum toroidal algebras and solvable structures in gauge/string theory
• Correlation functions with fusion-channel multiplicity in W3 Toda field theory
• Plane Partition Realization of (Web of) W-algebra Minimal Models
• Cylindric partitions, W_r characters and the Andrews-Gordon-Bressoud identities
• Matching branches of non-perturbative conformal block at its singularity divisor
• Gauge origami and quiver W-algebras
• Rigid Fuchsian systems in 2-dimensional conformal field theories
• $\widehat{\mathfrak{sl}}(n{)}_N$ WZW conformal blocks from $SU(N)$ instanton partition functions on ${\mathbb{C}}^2/{\mathbb{Z}}_n$
• Dessins d'Enfants, Seiberg-Witten Curves and Conformal Blocks
• From topological strings to minimal models
• $n$-th parafermion ${\mathcal{W}}_N$ characters from $U(N)$ instanton counting on ${\mathbb{C}}^2/{\mathbb{Z}}_n$
• Coloured refined topological vertices and parafermion conformal field theories
• AGT basis in SCFT for c=3/2 and Uglov Polynomials