A tauberian theorem for the conformal bootstrap
High Energy Physics - Theory
2018-01-17 v2 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.1709.00008,
title = {A tauberian theorem for the conformal bootstrap},
author = {Jiaxin Qiao and Slava Rychkov},
journal= {arXiv preprint arXiv:1709.00008},
year = {2018}
}
Comments
36pp; v2: refs and comments added, misprints corrected