Abstract
In this note, we derive a Mellin space version of the Lorentzian inversion formula for CFTs by explicitly integrating over the cross-ratios in d = 2 and d = 4 spacetime dimensions. We use the simplicity of the Mellin representation of Witten diagrams and the double discontinuity to find the OPE coefficients and anomalous dimensions of double- trace primaries in large N CFTs to order \( \frac{1}{N^4} \). We find that our results match analytically at order \( \frac{1}{N^2} \), and numerically at order \( \frac{1}{N^4} \) with existing literature.
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Dedicated to the memory of Joe Polchinski.
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Shyani, M. Lorentzian inversion and anomalous dimensions in Mellin space. J. High Energ. Phys. 2020, 71 (2020). https://doi.org/10.1007/JHEP09(2020)071
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DOI: https://doi.org/10.1007/JHEP09(2020)071