A conformal dispersion relation: correlations from absorption
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Publication:1995056
DOI10.1007/JHEP09(2020)009zbMATH Open1454.81182arXiv1910.12123MaRDI QIDQ1995056
Author name not available (Why is that?)
Publication date: 18 February 2021
Published in: (Search for Journal in Brave)
Abstract: We introduce the analog of Kramers-Kronig dispersion relations for correlators of four scalar operators in an arbitrary conformal field theory. The correlator is expressed as an integral over its 'absorptive part', defined as a double discontinuity, times a theory-independent kernel which we compute explicitly. The kernel is found by resumming the data obtained by the Lorentzian inversion formula. For scalars of equal scaling dimensions, it is a remarkably simple function (elliptic integral function) of two pairs of cross-ratios. We perform various checks of the dispersion relation (generalized free fields, holographic theories at tree-level, 3D Ising model), and get perfect matching. Finally, we derive an integral relation that relates the 'inverted' conformal block with the ordinary conformal block.
Full work available at URL: https://arxiv.org/abs/1910.12123
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