[Paper Review] Reggeization of N=8 Supergravity and N=4 Yang-Mills Theory II

Howard J. Schnitzer|arXiv (Cornell University)|Jun 7, 2007

Black Holes and Theoretical Physics14 references18 citations

TL;DR

This paper investigates the Regge behavior of N=4 Yang-Mills theory and N=8 supergravity via summation of ladder diagrams in the Regge limit. It shows that the graviton reggeizes with a trajectory passing through J=2, consistent with string-like Regge trajectories, and conjectures that infinite moving Regge cuts in non-planar diagrams may correspond to the infinite tower of massless states in the zero-slope limit of string theory, should N=8 supergravity be perturbatively finite.

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.

Motivation & Objective

• To investigate whether the graviton and gluon in N=8 supergravity and N=4 Yang-Mills theory reggeize in the Regge limit through summation of ladder diagrams.
• To determine if the Regge trajectory function in these theories is governed by the cusp anomalous dimension, particularly under the BDS conjecture for planar scattering.
• To explore the origin and structure of moving Regge cuts in non-planar diagrams, especially in N=8 supergravity.
• To examine the potential connection between these Regge cuts and the infinite tower of massless or low-mass states found in the zero-slope limit of string theory.

Proposed method

• Summing ladder diagrams in the leading logarithmic approximation for gluon-gluon and graviton-graviton scattering in the Regge limit.
• Using the KLT relations to relate N=4 YM theory to N=8 supergravity, transferring reggeization properties from gluons to gravitons.
• Applying analyticity and Mandelstam counting to argue for all-order reggeization, even beyond leading order.
• Analyzing non-planar diagrams to identify contributions to moving Regge cuts via multiple exchanges of Regge poles or cuts.
• Deriving the singularity structure of Regge cuts in the complex angular momentum plane using integrals over s1 and s2 with λ(s,s1,s2) in the denominator.
• Assuming linear Regge trajectories (α(s) = α(0) + α′s) to determine the positions of singularities and their accumulation near s=0.

Experimental results

Research questions

• RQ1 Does the summation of ladder diagrams in N=4 Yang-Mills theory reproduce the correct Regge limit, with the trajectory function proportional to the cusp anomalous dimension under the BDS conjecture?
• RQ2 Can the graviton in N=8 supergravity be shown to lie on a Regge trajectory, and does this trajectory pass through J=2 as expected for a closed string state?
• RQ3 What is the origin and structure of moving Regge cuts in N=8 supergravity, and how do they arise from non-planar diagrams?
• RQ4 Do the infinite moving Regge cuts in N=8 supergravity, accumulating near s=0, correspond to the infinite tower of massless states in the zero-slope limit of string theory?
• RQ5 Is the presence of such cuts a necessary signature of a perturbatively finite N=8 supergravity that is non-perturbatively consistent or in the swampland?

Key findings

• The graviton in N=8 supergravity reggeizes with a trajectory passing through J=2 in the Regge limit, consistent with string theory expectations.
• For N=4 Yang-Mills theory, under the BDS conjecture, the ladder sum reproduces the Regge limit with the trajectory function replaced by the cusp anomalous dimension.
• Non-planar diagrams in N=8 supergravity generate an infinite number of moving Regge cuts, with singularities accumulating near s=0.
• The positions of these cuts are given by j = nα(s/n²) - (n-1) for n = 1,2,3,…, and all pass through j=1 at s=0 when α(0)=1.
• The structure of these cuts suggests a possible link to the infinite tower of massless states in the zero-slope limit of string theory, as discussed by Green et al.
• If N=8 supergravity is perturbatively finite, the existence of these cuts may signal the emergence of string-like physics, including non-perturbative consistency or swampland constraints.