Conformal Regge theory

TL;DR

This paper extends Regge theory to conformal field theories using Mellin amplitudes, providing new insights into correlation functions, OPE coefficients, and the Regge trajectory at both weak and strong coupling regimes.

Contribution

It develops a conformal partial wave expansion in Mellin space and applies it to N=4 Super Yang Mills, predicting OPE behavior and refining the understanding of the Regge trajectory at various couplings.

Findings

Predicted OPE coefficients at high order in 't Hooft coupling.

Improved the understanding of the AdS graviton Regge trajectory.

Computed the strong coupling limit of OPE coefficients using flat space limit.

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.