Lorentzian inversion and anomalous dimensions in Mellin space
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...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-09-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | http://link.springer.com/article/10.1007/JHEP09(2020)071 |
| Summary: | 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 1 N 4 $$ \frac{1}{N^4} $$ . We find that our results match analytically at order 1 N 2 $$ \frac{1}{N^2} $$ , and numerically at order 1 N 4 $$ \frac{1}{N^4} $$ with existing literature. |
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| ISSN: | 1029-8479 |