Conformal Regge theory

Abstract

We generalize Regge theory to correlation functions in conformal field theories. This is done by exploring the analogy between Mellin amplitudes in AdS/CFT and S-matrix elements. In the process, we develop the conformal partial wave expansion in Mellin space, elucidating the analytic structure of the partial amplitudes. We apply the new formalism to the case of four point correlation functions between protected scalar operators in N=4 Super Yang Mills, in cases where the Regge limit is controlled by the leading twist operators associated to the pomeron-graviton Regge trajectory. At weak coupling, we are able to predict to arbitrary high order in the 't Hooft coupling the behaviour near J=1 of the OPE coefficients C_{OOJ} between the external scalars and the spin J leading twist operators. At strong coupling, we use recent results for the anomalous dimension of the leading twist operators to improve current knowledge of the AdS graviton Regge trajectory - in particular, determining the next and next to next leading order corrections to the intercept. Finally, by taking the flat space limit and considering the Virasoro-Shapiro S-matrix element, we compute the strong coupling limit of the OPE coefficient C_{LLJ} between two Lagrangians and the leading twist operators of spin J.

27 + 24 pages, 7 figures; v2 Typos corrected, references added; v3 Typo corrected; v4 Typos corrected, references added

References in corpus (14)

• Writing CFT correlation functions as AdS scattering amplitudes
• The Pomeron and Gauge/String Duality
• Dressing and Wrapping
• D-independent representation of Conformal Field Theories in D dimensions via transformation to auxiliary Dual Resonance Models. Scalar amplitudes
• AdS Field Theory from Conformal Field Theory
• Saturation in Deep Inelastic Scattering from AdS/CFT
• Eikonal Methods in AdS/CFT: Regge Theory and Multi-Reggeon Exchange
• String-Gauge Dual Description of Deep Inelastic Scattering at Small-$x$
• Analytic continuation of the Mellin moments of deep inelastic structure functions
• Black holes and universality classes of critical points
• Three-loop universal structure constants in N=4 susy Yang-Mills theory
• Using HERA Data to Determine the Infrared Behaviour of the BFKL Amplitude
• Holographic three-point functions for short operators
• Three-Point Functions of Twist-Two Operators in N=4 SYM at One Loop

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