Four-point conformal blocks with three heavy background operators

Abstract

We study CFT${}_2$ Virasoro conformal blocks of the 4-point correlation function $⟨{\mathcal{O}}_L{\mathcal{O}}_H{\mathcal{O}}_H{\mathcal{O}}_H⟩$ with three background operators ${\mathcal{O}}_H$ and one perturbative operator ${\mathcal{O}}_L$ of dimensions ${\Delta }_L/{\Delta }_H\ll 1$. The conformal block function is calculated in the large central charge limit using the monodromy method. From the holographic perspective, the background operators create $Ad{S}_3$ space with three conical singularities parameterized by dimensions ${\Delta }_H$, while the perturbative operator corresponds to the geodesic line stretched from the boundary to the bulk. The geodesic length calculates the perturbative conformal block. We propose how to address the block/length correspondence problem in the general case of higher-point correlation functions $⟨{\mathcal{O}}_L\cdots {\mathcal{O}}_L{\mathcal{O}}_H\cdots {\mathcal{O}}_H⟩$ with arbitrary numbers of background and perturbative operators.

arXiv comment21 pages, 2 figures, v2:typos corrected, journal version

References in corpus (29)

• A Stress Tensor for Anti-de Sitter Gravity
• Universality of Long-Distance AdS Physics from the CFT Bootstrap
• Analytic Continuation of Liouville Theory
• Virasoro Conformal Blocks and Thermality from Classical Background Fields
• Three-dimensional quantum geometry and black holes
• Holographic Entanglement Entropy from 2d CFT: Heavy States and Local Quenches
• Time evolution of entanglement entropy from a pulse
• Higher Spin Entanglement and W_N Conformal Blocks
• Monodromic vs geodesic computation of Virasoro classical conformal blocks
• Higher-point conformal blocks and entanglement entropy in heavy states
• Classical conformal blocks via AdS/CFT correspondence
• Exact Virasoro Blocks from Wilson Lines and Background-Independent Operators
• From global to heavy-light: 5-point conformal blocks
• An Exact Operator That Knows Its Location
• 3D Gravity, Point Particles and Liouville Theory
• Virasoro vacuum block at next-to-leading order in the heavy-light limit
• Holographic interpretation of 1-point toroidal block in the semiclassical limit
• Many-point classical conformal blocks and geodesic networks on the hyperbolic plane
• Liouville theory and uniformization of four-punctured sphere
• Holographic Description of 2D Conformal Block in Semi-classical Limit
• Multi-centered AdS${}_3$ solutions from Virasoro conformal blocks
• Holographic duals of large-c torus conformal blocks
• Perturbative classical conformal blocks as Steiner trees on the hyperbolic disk
• Large $c$ Virasoro Blocks from Monodromy Method beyond Known Limits
• New Properties of Large-$c$ Conformal Blocks from Recursion Relation
• Various semiclassical limits of torus conformal blocks
• Large-c superconformal torus blocks
• Geodesic description of Heavy-Light Virasoro blocks
• Holographic relations for OPE blocks in excited states

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• Bootstrapping closed string field theory
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• Towards $W_3$ classical blocks with semi-degenerate operators
• Differential equations for classical Virasoro blocks with heavy and light operators