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- W3100013149 abstract "We analyze modular invariance drawing inspiration from tauberian theorems. Given a modular invariant partition function with a positive spectral density, we derive lower and upper bounds on the number of operators within a given energy interval. They are most revealing at high energies. In this limit we rigorously derive the Cardy formula for the microcanonical entropy together with optimal error estimates for various widths of the averaging energy shell. We identify a new universal contribution to the microcanonical entropy controlled by the central charge and the width of the shell. We derive an upper bound on the spacings between Virasoro primaries. Analogous results are obtained in holographic 2d CFTs. We also study partition functions with a UV cutoff. Control over error estimates allows us to probe operators beyond the unity in the modularity condition. We check our results in the 2d Ising model and the Monster CFT and find perfect agreement." @default.
- W3100013149 created "2020-11-23" @default.
- W3100013149 creator A5022232479 @default.
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- W3100013149 date "2019-10-01" @default.
- W3100013149 modified "2023-10-17" @default.
- W3100013149 title "Modular invariance, tauberian theorems and microcanonical entropy" @default.
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- W3100013149 doi "https://doi.org/10.1007/jhep10(2019)261" @default.
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