Abstract
Modular covariance of torus one-point functions constrains the three point function coefficients of a two dimensional CFT. This leads to an asymptotic formula for the average value of light-heavy-heavy three point coefficients, generalizing Cardy’s formula for the high energy density of states. The derivation uses certain asymptotic properties of one-point conformal blocks on the torus. Our asymptotic formula matches a dual AdS3 computation of one point functions in a black hole background. This is evidence that the BTZ black hole geometry emerges upon course-graining over a suitable family of heavy microstates.
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ArXiv ePrint: 1608.03284
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Kraus, P., Maloney, A. A cardy formula for three-point coefficients or how the black hole got its spots. J. High Energ. Phys. 2017, 160 (2017). https://doi.org/10.1007/JHEP05(2017)160
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DOI: https://doi.org/10.1007/JHEP05(2017)160