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arXiv · 1709.00008

A tauberian theorem for the conformal bootstrap

Jiaxin Qiao·Slava Rychkov
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Abstract

For expansions in one-dimensional conformal blocks, we provide a rigorous link between the asymptotics of the spectral density of exchanged primaries and the leading singularity in the crossed channel. Our result has a direct application to systems of SL(2,R)-invariant correlators (also known as 1d CFTs). It also puts on solid ground a part of the lightcone bootstrap analysis of the spectrum of operators of high spin and bounded twist in CFTs in d>2. In addition, a similar argument controls the spectral density asymptotics in large N gauge theories.

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Jiaxin Qiao, Slava Rychkov. 2017-10-23. A tauberian theorem for the conformal bootstrap. https://doi.org/10.1007/jhep12(2017)119

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