High Energy Bounds on Soft N=4 SYM Amplitudes from AdS/CFT

TL;DR

This paper uses AdS/CFT correspondence to derive bounds on the high-energy behavior of N=4 SYM scattering amplitudes, connecting gravitational duality with unitarity constraints to establish an upper limit on the Pomeron intercept.

Contribution

It provides the first bounds on the high-energy scattering amplitude in N=4 SYM from AdS/CFT, incorporating unitarity and analyticity constraints, and explores the impact of various approximations.

Findings

Bound on Pomeron intercept: alpha ≤ 11/7.

Elastic eikonal approximation suggests alpha between 4/3 and 11/7.

Identification of divergences in supergravity contributions and their implications.

Abstract

Using the AdS/CFT correspondence, we study the high-energy behavior of colorless dipole elastic scattering amplitudes in N=4 SYM gauge theory through the Wilson loop correlator formalism and Euclidean to Minkowskian analytic continuation. The purely elastic behavior obtained at large impact-parameter L, through duality from disconnected AdS_5 minimal surfaces beyond the Gross-Ooguri transition point, is combined with unitarity and analyticity constraints in the central region. In this way we obtain an absolute bound on the high-energy behavior of the forward scattering amplitude due to the graviton interaction between minimal surfaces in the bulk. The dominant "Pomeron" intercept is bounded by alpha less than or equal to 11/7 using the AdS/CFT constraint of a weak gravitational field in the bulk. Assuming the elastic eikonal approximation in a larger impact-parameter range gives alpha between 4/3 and 11/7. The actual intercept becomes 4/3 if one assumes the elastic eikonal approximation within its maximally allowed range L larger than exp{Y/3}, where Y is the total rapidity. Subleading AdS/CFT contributions at large impact-parameter due to the other d=10 supergravity fields are obtained. A divergence in the real part of the tachyonic KK scalar is cured by analyticity but signals the need for a theoretical completion of the AdS/CFT scheme.