Geodesic description of Heavy-Light Virasoro blocks

Abstract

We continue to investigate the dual description of the Virasoro conformal blocks arising in the framework of the classical limit of the AdS${}_3$/CFT${}_2$ correspondence. To give such an interpretation in previous studies, certain restrictions were necessary. Our goal here is to consider more general situation available through the worldline approximation to the dual AdS gravity. Namely, we are interested in computing the spherical conformal blocks without the previously imposed restrictions on the conformal dimensions of the internal channels. The duality is realised as an equality of the so-called heavy-light limit of the n-point conformal block and the action of n-2 particles propagating in some AdS-like background with either a conical singularity or a BTZ black hole. We describe a procedure that allows relaxing the constraint on the intermediate channels. To obtain an explicit expression for the conformal block on the CFT side, we use a recently proposed recursion procedure and find full agreement between the results of the boundary and bulk computations.

arXiv comment13 pages, v3: refs added, typos removed

References in corpus (24)

• The Black Hole in Three Dimensional Space Time
• Universality of Long-Distance AdS Physics from the CFT Bootstrap
• Virasoro Conformal Blocks and Thermality from Classical Background Fields
• Entanglement Entropy at Large Central Charge
• Loops in AdS from Conformal Field Theory
• Quantum Entanglement of Localized Excited States at Finite Temperature
• A Cardy Formula for Three-Point Coefficients: How the Black Hole Got its Spots
• Semiclassical Virasoro Blocks from AdS${}_3$ Gravity
• Monodromic vs geodesic computation of Virasoro classical conformal blocks
• Scrambling time from local perturbations of the eternal BTZ black hole
• Higher-point conformal blocks and entanglement entropy in heavy states
• Classical conformal blocks via AdS/CFT correspondence
• From global to heavy-light: 5-point conformal blocks
• Poking Holes in AdS/CFT: Bulk Fields from Boundary States
• On the Late-Time Behavior of Virasoro Blocks and a Classification of Semiclassical Saddles
• Holographic Conformal Partial Waves as Gravitational Open Wilson Networks
• Holographic conformal blocks from interacting Wilson lines
• Holographic interpretation of 1-point toroidal block in the semiclassical limit
• Many-point classical conformal blocks and geodesic networks on the hyperbolic plane
• Holographic Description of 2D Conformal Block in Semi-classical Limit
• Multi-centered AdS${}_3$ solutions from Virasoro conformal blocks
• Various semiclassical limits of torus conformal blocks
• Lambda<0 Quantum Gravity in 2+1 Dimensions I: Quantum States and Stringy S-Matrix
• Exact partition functions for deformed $\mathcal{N}=2$ theories with $N_f=4$ flavours

Cited by in corpus (12)

• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Holographic duals of large-c torus conformal blocks
• Perturbative classical conformal blocks as Steiner trees on the hyperbolic disk
• Bootstrapping closed string field theory
• Scalar Blocks as Gravitational Wilson Networks
• Holographic variables for CFT${}_2$ conformal blocks with heavy operators
• More on Wilson toroidal networks and torus blocks
• Large-c superconformal torus blocks
• Four-point conformal blocks with three heavy background operators
• Semiclassical torus blocks in the t-channel
• Wilson lines construction of $\mathfrak{osp}(1|2)$ conformal blocks
• Large-$c$ conformal $(n\le 6)$-point blocks with superlight weights and holographic Steiner trees