Virasoro conformal blocks in closed form

By Eric Perlmutter. 2015

149 citations recorded by the source corpus.

A bstractVirasoro conformal blocks are fixed in principle by symmetry, but a closed-form expression is unknown in the general case. In this work, we provide two new closed-form expansions for the four-point Virasoro blocks on the sphere, for arbitrary operator dimensions and central charge c. We do so by solving known recursion relations. One representation is a sum over hypergeometric global blocks, whose coefficients we provide at arbitrary level. The other is a sum over semiclassical Virasoro blocks obtained in the limit in which two external operator dimensions scale linearly with large c. In both cases, the 1/c expansion of the Virasoro blocks is easily extracted. We discuss applications of these expansions to entanglement and thermality in conformal field theories and particle scattering in three-dimensional quantum gravity.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/19f13ddaf5d24772dd8b41f48a5538f71b50a7c6

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Citations in the corpus

Low-dimensional de Sitter quantum gravity (2019, methodology): “The model arising from Euclidean AdS3 computes Virasoro identity blocks [36, 103–109], and provides another method to calculate Virasoro Wilson lines [110–115].”
Black hole collapse in the 1/c expansion (2016, background): “(See also [12–15] for earlier work in this direction, and [16–39] for related developments and applications.”
Semiclassical Virasoro blocks from AdS3 gravity (2015, unknown): “These recursion relations can be solved [23, 24].”