Eikonal Methods in AdS/CFT: BFKL Pomeron at Weak Coupling

TL;DR

This paper investigates high-energy correlators in N=4 super Yang Mills within AdS/CFT, focusing on the weak coupling BFKL pomeron and its implications for unitarity and saturation phenomena.

Contribution

It provides a detailed position space analysis of the BFKL pomeron in AdS/CFT, highlighting conformal constraints and proposing a novel AdS eikonal resummation approach.

Findings

Pomeron exchange analyzed in position space with conformal symmetry constraints.

Weak coupling pomeron corresponds to BFKL dynamics in AdS/CFT.

Suggests a new AdS eikonal resummation differing from 4D exponentiation.

Abstract

We consider correlators of N=4 super Yang Mills of the form A ~ < O_1 O_2 O*_1 O*_2 >, where the operators O_1 and O_2 are scalar primaries. In particular, we analyze this correlator in the planar limit and in a Lorentzian regime corresponding to high energy interactions in AdS. The planar amplitude is dominated by a Regge pole whose nature varies as a function of the 't Hooft coupling g^2. At large g, the pole corresponds to graviton exchange in AdS, whereas at weak g, the pole is that of the hard perturbative BFKL pomeron. We concentrate on the weak coupling regime and analyze pomeron exchange directly in position space. The analysis relies heavily on the conformal symmetry of the transverse space E^2 and of its holographic dual hyperbolic space H_3, describing with an unified language, both the weak and strong 't Hooft coupling regimes. In particular, the form of the impact factors is highly constrained in position space by conformal invariance. Finally, the analysis suggests a possible AdS eikonal resummation of multi-pomeron exchanges implementing AdS unitarity, which differs from the usual 4-dimensional eikonal exponentiation. Relations to violations of 4-dimensional unitarity at high energy and to the onset of nonlinear effects and gluon saturation become immediate questions for future research.