Various semiclassical limits of torus conformal blocks

Abstract

We study four types of one-point torus blocks arising in the large central charge regime. According to different limits of conformal dimensions we distinguish between the global block, the light block, the heavy-light block, and the linearized classical block. We show that they are not independent and connected to each other by various links. We find that the global, light, and heavy-light blocks correspond to three different contractions of the Virasoro algebra. Also, we formulate the c-recursive representation of the one-point torus blocks which is relevant in the semiclassical approximation.

23 pages

References in corpus (5)

• Many-point classical conformal blocks and geodesic networks on the hyperbolic plane
• Holographic Description of 2D Conformal Block in Semi-classical Limit
• Classical irregular block, N=2 pure gauge theory and Mathieu equation
• Multi-centered AdS${}_3$ solutions from Virasoro conformal blocks
• Conformal perturbation theory and higher spin entanglement entropy on the torus

Cited by in corpus (13)

• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Witten Diagrams for Torus Conformal Blocks
• Holographic duals of large-c torus conformal blocks
• Perturbative classical conformal blocks as Steiner trees on the hyperbolic disk
• Discreteness and Integrality in Conformal Field Theory
• Large-c superconformal torus blocks
• Geodesic description of Heavy-Light Virasoro blocks
• Monodromy methods for torus conformal blocks and entanglement entropy at large central charge
• More on Wilson toroidal networks and torus blocks
• BMS Modular Diaries: Torus one-point function
• Four-point conformal blocks with three heavy background operators
• Semiclassical torus blocks in the t-channel
• c-Recursion for multi-point superconformal blocks. NS sector