Reggeization of N=8 Supergravity and N=4 Yang-Mills Theory II
Howard J. Schnitzer
TL;DR
This work analyzes Regge behavior in the ladder-graph sector of $\mathcal{N}=4$ Yang-Mills theory and $\mathcal{N}=8$ supergravity by summing leading-log ladders in the Regge limit. Using KLT relations, it shows graviton reggeization and, under planar assumptions, gluon reggeization tied to the cusp anomalous dimension, while Regge cuts arise from non-planar graphs. Gravitons lie on moving Regge trajectories through $J=2$ with trajectory $\alpha(s)$ governed by ladder sums, and non-planar exchanges generate an infinite family of Regge cuts that may connect to the Green–Ooguri–Schwarz massless spectrum. The results hint that perturbative stringy phenomena could be encoded in $\mathcal{N}=8$ sugra ladder sectors, while highlighting IR subtleties for the gauge theory and unresolved questions about non-perturbative consistency.
Abstract
The loop expansion for the n-point functions of N=4 Yang-Mills theory and N=8 supergravity can be formulated as the loop expansion of scalar field theory with an infinite subclass being the ladder diagrams. We consider the sum of ladder diagrams for gluon-gluon and graviton-graviton scattering in the Regge limit. The reggeization of the gluon and the graviton is discussed in this context and that of hep-th/0701217. If the Bern, Dixon, Smirnov conjecture for planar gluon-gluon scattering is correct, then the ladder sum for SU(N) gauge theory at large N, correctly gives the Regge limit, with Regge trajectory function proportional to the cusp anomalous dimension. In graviton-graviton scattering it is argued that the graviton lies on a Regge trajectory. Regge cuts are also present due to infinite sums of non-planar graphs. The multiple exchange of Regge poles in non-planar graphs can give a countable infinite number of moving Regge cuts which accumulate near s=0. It is conjectured that this may be related to the infinite number of non-perturbative massless states which remain in the limit discussed by Green, Ooguri and Schwarz.