Towards $W_3$ classical blocks with semi-degenerate operators

Abstract

We consider 4-point $W_3$ classical blocks focusing on the blocks level-1 and level-2 semi-degenerate operators. We derive BPZ-type equations for the auxiliary 5-point blocks with one additional fully degenerate operator. The monodromy properties of these equations are encoded by the accessory parameters, related to the 4-point $W_3$ classical blocks. We solve the BPZ-type equations via heavy-light perturbation theory and find the accessory parameters, which allows us to obtain the explicit expressions for the considered class of classical blocks.

19 pages, 2 figures, v2: typos corrected, references and acknowledgments added; v3: minor changes, the content matches the version published in Nuclear Physics B, 20 pages, 2 figures

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