CFT exercises for the needs of AGT

Abstract

An explicit check of the AGT relation between the W_N-symmetry controlled conformal blocks and U(N) Nekrasov functions requires knowledge of the Shapovalov matrix and various triple correlators for W-algebra descendants. We collect simplest expressions of this type for N=3 and for the two lowest descendant levels, together with the detailed derivations, which can be now computerized and used in more general studies of conformal blocks and AGT relations at higher levels.

29 pages

References in corpus (7)

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• Factorization of differential expansion for antiparallel double-braid knots
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• Perspectives of differential expansion
• Matching branches of non-perturbative conformal block at its singularity divisor
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• On exclusive Racah matrices $\bar{S}$ for rectangular representations
• Cut-and-join operators and Macdonald polynomials from the 3-Schur functions
• Invariants of knots and links at roots of unity