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A tauberian theorem for the conformal bootstrap

Jiaxin Qiao, Slava Rychkov

31/8/17 Published in : arXiv:1709.00008

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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  • Field Theory
  • Statistical Mechanics

The complex side of the TS/ST correspondence

From Hartree dynamics to the relativistic Vlasov equation

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