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arXiv · 1908.00015

Lorentzian inversion and anomalous dimensions in Mellin space

Milind Shyani
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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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Milind Shyani. 2019-07-31. Lorentzian inversion and anomalous dimensions in Mellin space. https://arxiv.org/abs/1908.00015

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