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.