Virasoro blocks at large exchange dimension

Abstract

In this paper, we analyze Virasoro conformal blocks in the limit when the operator exchange dimension is taking to be large in comparison with the other parameters dependence of the block. We do this by using Zamolodchikov's recursion relations. We found a dramatically simplified solution at leading order in an inverse power expansion in large exchange conformal dimension in terms of a quasi-modular form in an Eisenstein series representation. We compare this solution with existing results obtained previously by using AGT correspondence.

arXiv comment20 pages, No figures. References and acknowledgments updated. Subsection (4.2) added, appendix added. Version matching journal version

References in corpus (33)

• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Structure Constants and Conformal Bootstrap in Liouville Field Theory
• Symmetries of asymptotically flat 4 dimensional spacetimes at null infinity revisited
• Applied Conformal Field Theory
• A SUSY SU(5) Grand Unified Model of Tri-Bimaximal Mixing from A4
• Semiclassical Virasoro Symmetry of the Quantum Gravity S-Matrix
• Virasoro Conformal Blocks and Thermality from Classical Background Fields
• Clebsch-Gordan and Racah-Wigner coefficients for a continuous series of representations of U_q(sl(2,R))
• Large Spin Perturbation Theory
• On combinatorial expansion of the conformal blocks arising from AGT conjecture
• Liouville bootstrap via harmonic analysis on a noncompact quantum group
• $d$-dimensional SYK, AdS Loops, and $6j$ Symbols
• Recursion relations in CFT and N=2 SYM theory
• On AGT conjecture
• The Omega deformed B-model for rigid N=2 theories
• Recursive representation of the torus 1-point conformal block
• Search for the ${\Lambda }_b\to \Lambda {\eta }^{\prime }$ and ${\Lambda }_b\to \Lambda \eta$ decays with the LHCb detector
• Classical Conformal Blocks and Painleve VI
• Conformal Bootstrap, Universality and Gravitational Scattering
• Quantum Regge Trajectories and the Virasoro Analytic Bootstrap
• Semiclassical Virasoro Blocks from AdS${}_3$ Gravity
• Isomonodromic tau-functions from Liouville conformal blocks
• A non-rational CFT with c=1 as a limit of minimal models
• Eikonalization of Conformal Blocks
• Hawking from Catalan
• A Numerical Approach to Virasoro Blocks and the Information Paradox
• Deformed N=2 theories, generalized recursion relations and S-duality
• Differential equation for four-point correlation function in Liouville field theory and elliptic four-point conformal blocks
• Virasoro vacuum block at next-to-leading order in the heavy-light limit
• Modular crossings, OPE coefficients and black holes
• Semi-classical Virasoro blocks: proof of exponentiation
• Anomalous dimensions at finite conformal spin from OPE inversion
• Transformations of Spherical Blocks

Cited by in corpus (3)

• Universality in asymptotic bounds and its saturation in $2$D CFT
• More on Wilson toroidal networks and torus blocks
• Four-point correlation modular bootstrap for OPE densities