Lorentzian inversion and anomalous dimensions in Mellin space

A bstract 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 th...

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Veröffentlicht in:	The journal of high energy physics 2020-09, Vol.2020 (9), p.1-30, Article 71
1. Verfasser:	Shyani, Milind
Format:	Artikel
Sprache:	eng
Schlagworte:	AdS-CFT Correspondence Classical and Quantum Gravitation Conformal Field Theory Elementary Particles Physics Physics and Astronomy Quantum Field Theories Quantum Field Theory Quantum Physics Regular Article - Theoretical Physics Relativity Theory String Theory
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Zusammenfassung:	A bstract 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 . We find that our results match analytically at order 1 N 2 , and numerically at order 1 N 4 with existing literature.
ISSN:	1029-8479 1029-8479
DOI:	10.1007/JHEP09(2020)071