Holographic duals of large-c torus conformal blocks

Abstract

We study CFT2 conformal blocks on a torus and their holographic realization. The classical conformal blocks arising in the regime where conformal dimensions grow linearly with the large central charge are shown to be holographically dual to the geodesic networks stretched in the thermal AdS bulk space. We discuss the n-point conformal blocks and their duals, the 2-point case is elaborated in full detail. We develop various techniques to calculate both quantum and classical conformal block functions. In particular, we show that exponentiated global torus blocks reproduce classical torus blocks in the specific perturbative regimes of the conformal parameter space.

arXiv comment37 pages, v2: more comments, Appendix E --> Section 7.1, refs added, journal version

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• A slow review of the AGT correspondence
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• Bands and gaps in Nekrasov partition function
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• Rényi entropy of single-character CFTs on the torus