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Title:
High-Energy Bootstrap and Tauberian Theory
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Abstract:
We discuss 2d modular invariant CFT partition functions. Using ideas of tauberian theory we rigorously derive Cardy formula with corrections and error estimates with or without fixing the spin of operators. The result depends on the size of the averaging window in the microcanonical entropy. As a byproduct, we show that the largest spacing between neighboring energy eigenstates at asymptotically high energies is 1. In chaotic theories the spacing is expected to be small. This is related to the fact that the spectral form-factor decays for a long time.
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