QCD at High Energies and Two-Dimensional Field Theory

TL;DR

This paper derives a simplified effective model for high-energy QCD scattering, revealing its two-dimensional nature and connecting it with sigma-models on the transverse plane, consistent with known perturbative results.

Contribution

It formulates a (3+1)-dimensional effective theory at high energies that captures the two-dimensional interactions of QCD, extending previous work and clarifying its relation to Lipatov's vertex.

Findings

Effective theory reduces to a two-dimensional sigma-model on the transverse plane.

The model is consistent with perturbative QCD results.

Clarifies the connection with Lipatov's gluon emission vertex.

Abstract

Previous studies of high-energy scattering in QCD have shown a remarkable correspondence with two-dimensional field theory. In this paper we formulate a simple effective model in which this two-dimensional nature of the interactions is manifest. Starting from the (3+1)-dimensional Yang-Mills action, we implement the high energy limit $s\! >\! > \! t$ via a scaling argument and we derive from this a simplified effective theory. This effective theory is still (3+1)-dimensional, but we show that its interactions can to leading order be summarized in terms of a two-dimensional sigma-model defined on the transverse plane. Finally, we verify that our formulation is consistent with known perturbative results. This is a revised and extended version of hep-th 9302104. In particular, we have added a section that clarifies the connection with Lipatov's gluon emission vertex.