The Regge limit for Green functions in conformal field theory

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 [32-35], 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 [39, 40], BFKL [24-26] 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.