Second level semi-degenerate fields in W3 Toda theory: matrix element and differential equation

Abstract

In a recent study we considered W3 Toda 4-point functions that involve matrix elements of a primary field with the highest-weight in the adjoint representation of sl3. We generalize this result by considering a semi-degenerate primary field, which has one null vector at level two. We obtain a sixth-order Fuchsian differential equation for the conformal blocks. We discuss the presence of multiplicities, the matrix elements and the fusion rules.

arXiv comment22 pages. Published JHEP version: Typos corrected, references added. Section 5.2.3 added

References in corpus (20)

• Liouville Correlation Functions from Four-dimensional Gauge Theories
• W-symmetry in Conformal Field Theory
• 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
• Correlation functions in conformal Toda field theory I
• Correlation functions in conformal Toda field theory II
• Super Liouville conformal blocks from N=2 SU(2) quiver gauge theories
• Vertices, Vortices & Interacting Surface Operators
• M2-brane surface operators and gauge theory dualities in Toda
• Conformal blocks in Virasoro and W theories: duality and the Calogero-Sutherland model
• AGT conjecture and Integrable structure of Conformal field theory for c=1
• Null vectors, 3-point and 4-point functions in conformal field theory
• Null vectors of the W_3 algebra
• Analysis of correlation functions in Toda theory and AGT-W relation for SU(3) quiver
• A2 Toda theory in reduced WZNW framework and the representations of the W algebra
• Correlation functions with fusion-channel multiplicity in W3 Toda field theory
• Fusion in the W_3 algebra
• Exact conformal blocks for the W-algebras, twist fields and isomonodromic deformations
• On some 3-point functions in the $W_4$ CFT and related braiding matrix

Cited by in corpus (8)

• Webs of W-algebras
• A slow review of the AGT correspondence
• Notes on the solutions of Zamolodchikov-type recursion relations in Virasoro minimal models
• Rigid Fuchsian systems in 2-dimensional conformal field theories
• The imaginary Toda field theory
• Towards $W_3$ classical blocks with semi-degenerate operators
• Fusion of spin fields in $W_3$ conformal field theories
• Differential equations for classical Virasoro blocks with heavy and light operators