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Title:
High-Energy Conformal Bootstrap and Tauberian Theory
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Abstract:
We analyze modular invariance drawing inspiration from tauberiantheorems. Given a modular invariant partition function with a positivespectral density, we derive lower and upper bounds on the number ofoperators within a given energy interval. They are most revealing at highenergies. In this limit we rigorously derive the Cardy formula for themicrocanonical entropy together with optimal error estimates for variouswidths of the averaging energy shell. Finally, we identify a new universalcontribution to the microcanonical entropy controlled by the centralcharge and the width of the shell.
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