Minimal surfaces and Reggeization in the AdS/CFT correspondence

TL;DR

This paper explores how minimal surfaces in AdS/CFT relate to scattering amplitudes involving Wilson lines and loops, revealing different behaviors in confining versus conformal theories and connecting Reggeization to the geometry of the dual space.

Contribution

It introduces a novel approach linking minimal surfaces in AdS space to scattering amplitudes, including Regge trajectories, in both confining and conformal gauge theories.

Findings

Reggeized amplitudes with linear trajectories are derived in confining theories.

Infra-red divergences can be factorized or cured by considering Wilson loop correlations.

A transition between confining and conformal regimes is identified based on impact parameter.

Abstract

We address the problem of computing scattering amplitudes related to the correlation function of two Wilson lines and/or loops elongated along light-cone directions in strongly coupled gauge theories. Using the AdS/CFT correspondence in the classical approximation, the amplitudes are shown to be related to minimal surfaces generalizing the {\em helicoid} in various $AdS_5$ backgrounds. Infra-red divergences appearing for Wilson lines can be factorized out or can be cured by considering the IR finite case of correlation functions of two Wilson loops. In non-conformal cases related to confining theories, reggeized amplitudes with linear trajectories and unit intercept are obtained and shown to come from the approximately flat metrics near the horizon, which sets the scale for the Regge slope. In the conformal case the absence of confinement leads to a different solution. A transition between both regimes appears, in a confining theory, when varying impact parameter.