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We consider Virasoro conformal blocks in the large central charge limit.There are different regimes depending on the behavior of the conformaldimensions. The most simple regime is reduced to the global sl(2, C) conformalblocks while the most complicated one is known as the classical conformalblocks. Recently, Fitzpatrick, Kaplan, and Walters showed that the two regimesare related through the intermediate stage of the so-called heavy-lightsemiclassical limit. We study this idea in the particular case of the 5-pointconformal block. To find the 5-point global block we use the projectortechnique and the Casimir operator approach. Furthermore, we discuss therelation between the global and the heavy-light limits and construct theheavy-light block from the global block. In this way we reproduce our previousresults for the 5-point perturbative classical block obtained by means of themonodromy method.

From global to heavy-light: 5-point conformal blocks