Lorentzian inversion and anomalous dimensions in Mellin space

• Main Author: Milind Shyani
• Format: Article
• Language: English
• Published: SpringerOpen 2020-09-01
• Series: Journal of High Energy Physics
• Subjects: AdS-CFT Correspondence; Conformal Field Theory
• Online Access: http://link.springer.com/article/10.1007/JHEP09(2020)071

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.