Abstract
We consider the semiclassical limit of the vacuum Virasoro block describing the diagonal 4-point correlation functions on the sphere. At large central charge c, after exponentiation, it depends on two fixed ratios h H /c and h L /c, where h H,L are the conformal dimensions of the 4-point function operators. The semiclassical block may be expanded in powers of the light ratio h L /c and the leading non-trivial (linear) order is known in closed form as a function of h H /c. Recently, this contribution has been matched against AdS3 gravity calculations where heavy operators build up a classical geometry corresponding to a BTZ black hole, while the light operators are described by a geodesic in this background. Here, we compute for the first time the next-to-leading quadratic correction \( \mathcal{O} \)((h L /c)2), again in closed form for generic heavy operator ratio h H /c. The result is a highly non-trivial extension of the leading order and may be relevant for further refined AdS3/CFT2 tests. Applications to the two-interval Rényi entropy are also presented.
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Beccaria, M., Fachechi, A. & Macorini, G. Virasoro vacuum block at next-to-leading order in the heavy-light limit. J. High Energ. Phys. 2016, 72 (2016). https://doi.org/10.1007/JHEP02(2016)072
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DOI: https://doi.org/10.1007/JHEP02(2016)072