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.

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

References in corpus (9)

• Entanglement Entropy at Large Central Charge
• Holographic Entanglement Entropy from 2d CFT: Heavy States and Local Quenches
• Quantum Entanglement of Localized Excited States at Finite Temperature
• On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
• AGT conjecture and Integrable structure of Conformal field theory for c=1
• Witten Diagrams for Torus Conformal Blocks
• Many-point classical conformal blocks and geodesic networks on the hyperbolic plane
• Holographic Description of 2D Conformal Block in Semi-classical Limit
• Geodesic description of Heavy-Light Virasoro blocks

Cited by in corpus (4)

• Semiclassical torus blocks in the t-channel
• Wilson lines construction of $\mathfrak{osp}(1|2)$ conformal blocks
• 3D $\mathcal{N}=1$ supergravity from Virasoro TQFT: Gravitational partition function and Out-of-time-order correlator
• Rényi entropy of single-character CFTs on the torus