# Higher point semi-classical Virasoro conformal blocks

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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• Could you be more specific? Can you give the arXiv numbers of the papers you are mentioning? You want all operators with the same dimension: light or heavy? What about the exchanged operators? – Sylvain Ribault Sep 14 '18 at 7:31
• I have edited the question accordingly. I am looking for n-point arbitrary light operator correlators. Although I am not completely clear, but I thought that in large c limit the main contribution comes only from identity exchange, but I might be wrong, so I have omitted that part in the question. – Jaswin Sep 14 '18 at 8:18

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 .