The large central charge limit of conformal blocks

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Abstract We study conformal blocks of conformal field theories with a W 3 symmetry algebra in the limit where the central charge is large. In this limit, we compute the fourpoint block as a special case of an sℓ 3-invariant function. In the case when two of the four fields are semi-degenerate, we check that our results agree with the block’s combinatorial expansion as a sum over Young diagrams. We also show that such a block obeys a sixthorder differential equation, and that it has an unexpected singularity at z = −1, in addition to the expected singularities at z = 0, 1, ∞.