I am looking for references of higher point semi-classical Virasoro Conformal blocks. I know of one paper where two heavy and arbitrary light operators(https://arxiv.org/abs/1601.06794) have been considered, and another paper with 5-point correlator(https://arxiv.org/abs/1512.07627) is considered. But I am particularly trying to find references/attempts with all equal dimensional operator light correlators. Are there any?
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In the light limit, there is no reason for the identity exchange to dominate. If all operators are light, including exchanged operators, an $N$-point block is a simple integral over $N-3$ variables. The case $N=4$ is given by formula (2.12) of https://arxiv.org/abs/1109.6764 , whose generalization to $N\geq 5$ is straightforward. It should also be possible to generalize the hypergeometric representation (2.13), I am not sure if this has been worked out explicitly. For $N=5$ this seems to be formula (2.10) of your reference https://arxiv.org/abs/1512.07627 .