C. Sleight, and M. Taronna. (2018)cite arxiv:1807.05941Comment: 55 pages, 2 figures. v3: Finite spin expressions included in general d. Connection underlined between Wilson polynomials, the spectral function in the conformal partial wave expansion, and the Wilson function. References added. v4: Improved presentation and typos fixed.
DOI: 10.1007/JHEP11(2018)089
Abstract
In this note we consider the problem of extracting the corrections to CFT
data induced by the exchange of a primary operator and its descendents in the
crossed channel. We show how those corrections which are analytic in spin can
be systematically extracted from crossing kernels. To this end, we underline a
connection between: Wilson polynomials (which naturally appear when considering
the crossing kernels given recently in arXiv:1804.09334), the spectral integral
in the conformal partial wave expansion, and Wilson functions. Using this
connection, we determine closed form expressions for the OPE data when the
external operators in 4pt correlation functions have spins $J_1$-$J_2$-$0$-$0$,
and in particular the anomalous dimensions of double-twist operators of the
type $O_J_1O_J_2_n,\ell$ in $d$ dimensions and for
both leading and sub-leading twist. The OPE data are expressed in terms of
Wilson functions, which naturally appear as a spectral integral of a Wilson
polynomial. As a consequence, our expressions are manifestly analytic in spin
and are valid up to finite spin. We present some applications to CFTs with
slightly broken higher-spin symmetry. The Mellin Barnes integral representation
for $6j$ symbols of the conformal group in general $d$ and its relation with
the crossing kernels are also discussed.
cite arxiv:1807.05941Comment: 55 pages, 2 figures. v3: Finite spin expressions included in general d. Connection underlined between Wilson polynomials, the spectral function in the conformal partial wave expansion, and the Wilson function. References added. v4: Improved presentation and typos fixed
%0 Generic
%1 sleight2018anomalous
%A Sleight, Charlotte
%A Taronna, Massimo
%D 2018
%K ads-cft
%R 10.1007/JHEP11(2018)089
%T Anomalous Dimensions from Crossing Kernels
%U http://arxiv.org/abs/1807.05941
%X In this note we consider the problem of extracting the corrections to CFT
data induced by the exchange of a primary operator and its descendents in the
crossed channel. We show how those corrections which are analytic in spin can
be systematically extracted from crossing kernels. To this end, we underline a
connection between: Wilson polynomials (which naturally appear when considering
the crossing kernels given recently in arXiv:1804.09334), the spectral integral
in the conformal partial wave expansion, and Wilson functions. Using this
connection, we determine closed form expressions for the OPE data when the
external operators in 4pt correlation functions have spins $J_1$-$J_2$-$0$-$0$,
and in particular the anomalous dimensions of double-twist operators of the
type $O_J_1O_J_2_n,\ell$ in $d$ dimensions and for
both leading and sub-leading twist. The OPE data are expressed in terms of
Wilson functions, which naturally appear as a spectral integral of a Wilson
polynomial. As a consequence, our expressions are manifestly analytic in spin
and are valid up to finite spin. We present some applications to CFTs with
slightly broken higher-spin symmetry. The Mellin Barnes integral representation
for $6j$ symbols of the conformal group in general $d$ and its relation with
the crossing kernels are also discussed.
@misc{sleight2018anomalous,
abstract = {In this note we consider the problem of extracting the corrections to CFT
data induced by the exchange of a primary operator and its descendents in the
crossed channel. We show how those corrections which are analytic in spin can
be systematically extracted from crossing kernels. To this end, we underline a
connection between: Wilson polynomials (which naturally appear when considering
the crossing kernels given recently in arXiv:1804.09334), the spectral integral
in the conformal partial wave expansion, and Wilson functions. Using this
connection, we determine closed form expressions for the OPE data when the
external operators in 4pt correlation functions have spins $J_1$-$J_2$-$0$-$0$,
and in particular the anomalous dimensions of double-twist operators of the
type $[\mathcal{O}_{J_1}\mathcal{O}_{J_2}]_{n,\ell}$ in $d$ dimensions and for
both leading and sub-leading twist. The OPE data are expressed in terms of
Wilson functions, which naturally appear as a spectral integral of a Wilson
polynomial. As a consequence, our expressions are manifestly analytic in spin
and are valid up to finite spin. We present some applications to CFTs with
slightly broken higher-spin symmetry. The Mellin Barnes integral representation
for $6j$ symbols of the conformal group in general $d$ and its relation with
the crossing kernels are also discussed.},
added-at = {2019-03-22T10:23:51.000+0100},
author = {Sleight, Charlotte and Taronna, Massimo},
biburl = {https://www.bibsonomy.org/bibtex/221e38630017c24886d4b61406e23a453/acastro},
description = {Anomalous Dimensions from Crossing Kernels},
doi = {10.1007/JHEP11(2018)089},
interhash = {71cfc8aaec8df9c9161a160042f7d772},
intrahash = {21e38630017c24886d4b61406e23a453},
keywords = {ads-cft},
note = {cite arxiv:1807.05941Comment: 55 pages, 2 figures. v3: Finite spin expressions included in general d. Connection underlined between Wilson polynomials, the spectral function in the conformal partial wave expansion, and the Wilson function. References added. v4: Improved presentation and typos fixed},
timestamp = {2019-03-22T10:23:51.000+0100},
title = {Anomalous Dimensions from Crossing Kernels},
url = {http://arxiv.org/abs/1807.05941},
year = 2018
}