Example of the $4$-pt non-vacuum ${\mathcal{W}}_3$ classical block

Abstract

In this note, we study a special case of the $4$-pt non-vacuum classical block associated with the ${\mathcal{W}}_3$ algebra. We formulate the monodromy problem for the block and derive monodromy equations within the heavy-light approximation. Fixing the remaining functional arbitrariness using parameters of the $4$-pt vacuum ${\mathcal{W}}_3$ block, we compute the $4$-pt non-vacuum ${\mathcal{W}}_3$ block function.

arXiv commentV2: 18 pages, typos corrected, comments and references added

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• Towards $W_3$ classical blocks with semi-degenerate operators