The Regge Limit for Green Functions in Conformal Field Theory

TL;DR

This paper introduces a new Regge limit for off-shell Green functions in conformal field theories, connecting weak and strong coupling regimes and providing a unified framework for analyzing high-energy scattering.

Contribution

It defines a novel Regge limit for off-shell Green functions in CFTs, extending previous definitions and linking weak and strong coupling analyses.

Findings

Reproduces the BFKL approach to the pomeron at weak coupling.

Defines the BFKL kernel via two-point functions of light-like bilocal operators.

Discusses gravity dual predictions for the Regge limit at strong coupling.

Abstract

We define a Regge limit for off-shell Green functions in quantum field theory, and study it in the particular case of conformal field theories (CFT). Our limit differs from that defined in arXiv:0801.3002, the latter being only a particular corner of the Regge regime. By studying the limit for free CFTs, we are able to reproduce the Low-Nussinov, BFKL approach to the pomeron at weak coupling. The dominance of Feynman graphs where only two high momentum lines are exchanged in the t-channel, follows simply from the free field analysis. We can then define the BFKL kernel in terms of the two point function of a simple light-like bilocal operator. We also include a brief discussion of the gravity dual predictions for the Regge limit at strong coupling.