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

Abstract

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

19 pages, v2: minor corrections, typos removed; v3: more comments, extended Introduction and Conclusion, refs added, journal version

References in corpus (5)

• Holographic Entanglement Entropy from 2d CFT: Heavy States and Local Quenches
• Entwinement and the emergence of spacetime
• Quantum Entanglement of Localized Excited States at Finite Temperature
• Virasoro vacuum block at next-to-leading order in the heavy-light limit
• Holographic Dual to Conical Defects: I. Moving Massive Particle

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