Virasoro conformal blocks in closed form

DOI10.1007/JHEP08(2015)088zbMATH Open1388.81690arXiv1502.07742OpenAlexW3100835958MaRDI QIDQ2635724

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Publication date: 31 May 2018

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Abstract: Virasoro conformal blocks are fixed in principle by symmetry, but a closed-form expression is unknown in the general case. In this work, we provide three 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. Another 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.

Full work available at URL: https://arxiv.org/abs/1502.07742

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