Analysis of correlation functions in Toda theory and AGT-W relation for SU(3) quiver

Abstract

We give some evidences of the AGT-W relation between SU(3) quiver gauge theories and A_2 Toda theory. In particular, we derive the explicit form of 5-point correlation functions in the lower orders and confirm the agreement with Nekrasov's partition function for SU(3)xSU(3) quiver gauge theory. The algorithm to derive the correlation functions can be applied to general n-point function in A_2 Toda theory which will be useful to establish the relation for more generic quivers. Partial analysis is also given for SU(3)xSU(2) case and we comment on some technical issues which need clarification before establishing the relation.

37 pages, 1 figure, ver.2: minor typos corrected

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• A slow review of the AGT correspondence
• Holographic duals of large-c torus conformal blocks
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• Second level semi-degenerate fields in W3 Toda theory: matrix element and differential equation
• Higher rank isomonodromic deformations and W-algebras
• Rigid Fuchsian systems in 2-dimensional conformal field theories
• Three- and four-point connectivities of two-dimensional critical $Q-$ Potts random clusters on the torus
• Notes on 3-point functions of A_{N-1} Toda theory and AGT-W relation for SU(N) quiver
• Wilson lines construction of ${\mathfrak{sl}}_3$ toroidal conformal blocks
• The imaginary Toda field theory
• The Euler anomaly and scale factors in Liouville/Toda CFTs
• A note on W symmetry of N=2 gauge theory