A basis of analytic functionals for CFTs in general dimension
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Publication:1980679
DOI10.1007/JHEP08(2021)140zbMATH Open1469.81064arXiv1910.12855OpenAlexW3206865385MaRDI QIDQ1980679
Author name not available (Why is that?)
Publication date: 8 September 2021
Published in: (Search for Journal in Brave)
Abstract: We develop an analytic approach to the four-point crossing equation in CFT, for general spacetime dimension. In a unitary CFT, the crossing equation (for, say, the s- and t-channel expansions) can be thought of as a vector equation in an infinite-dimensional space of complex analytic functions in two variables, which satisfy a boundedness condition in the u-channel Regge limit. We identify a useful basis for this space of functions, consisting of the set of s- and t-channel conformal blocks of double-twist operators in mean field theory. We describe two independent algorithms to construct the dual basis of linear functionals, and work out explicitly many examples. Our basis of functionals appears to be closely related to the CFT dispersion relation recently derived by Carmi and Caron-Huot.
Full work available at URL: https://arxiv.org/abs/1910.12855
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