Holographic variables for CFT${}_2$ conformal blocks with heavy operators

Abstract

We consider large-$c$ $n$-point Virasoro blocks with $n-k$ background heavy operators and $k$ perturbative heavy operators. Conformal dimensions of heavy operators scale linearly with large $c$, while splitting into background/perturbative operators assumes an additional perturbative expansion. Such conformal blocks can be calculated within the monodromy method that basically reduces to solving auxiliary Fuchsian second-order equation and finding monodromy of solutions. We show that there exist particular variables that we call holographic, use of which drastically simplifies the whole analysis. In consequence, we formulate the uniformization property of the large-$c$ blocks which states that in the holographic variables their form depends only on the number of perturbative heavy operators. On the other hand, the holographic variables encode the metric in the bulk space so that the conformal blocks with the same number of perturbative operators are calculated by the same geodesic trees but on different geometries created by the background operators.

arXiv comment21 pages, v3: More comments and explanations, new Fig. 1, references added. Journal version

References in corpus (23)

• Entanglement Entropy and Quantum Field Theory
• A Stress Tensor for Anti-de Sitter Gravity
• Entanglement entropy and conformal field theory
• Virasoro Conformal Blocks and Thermality from Classical Background Fields
• Analytic Continuation of Liouville Theory
• Entanglement Entropy at Large Central Charge
• Semiclassical Virasoro Blocks from AdS${}_3$ Gravity
• Time evolution of entanglement entropy from a pulse
• Multipoint Conformal Blocks in the Comb Channel
• Monodromic vs geodesic computation of Virasoro classical conformal blocks
• Higher-point conformal blocks and entanglement entropy in heavy states
• The BMS Bootstrap
• From global to heavy-light: 5-point conformal blocks
• Entanglement Entropy, OTOC and Bootstrap in 2D CFTs from Regge and Light Cone Limits of Multi-point Conformal Block
• Holographic dual of the five-point conformal block
• Phases of scrambling in eigenstates
• Semi-classical Virasoro blocks: proof of exponentiation
• From Conformal Blocks to Path Integrals in the Vaidya Geometry
• Many-point classical conformal blocks and geodesic networks on the hyperbolic plane
• Perturbative classical conformal blocks as Steiner trees on the hyperbolic disk
• Geodesic description of Heavy-Light Virasoro blocks
• Multi-Black Hole Sectors of AdS_3 Gravity
• Geometry of Black Holes and Multi-Black-Holes in 2+1 dimensions

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