Review of AdS/CFT Integrability, Chapter IV.4: Integrability in QCD and N<4 SYM

TL;DR

This review discusses how quantum-level hidden symmetries in QCD and related gauge theories reveal integrable structures, such as Heisenberg spin chains, influencing their scale dependence and high-energy scattering behaviors.

Contribution

It highlights the emergence of integrability in QCD and N=4 SYM at the quantum level, connecting gauge theory dynamics to integrable spin chain models.

Findings

QCD exhibits hidden quantum symmetries related to integrability.

Effective QCD dynamics can be described by integrable spin chain models.

Integrability explains scale dependence and high-energy behavior of scattering amplitudes.

Abstract

There is a growing amount of evidence that QCD (and four-dimensional gauge theories in general) possess a hidden symmetry which does not exhibit itself as a symmetry of classical Lagrangians but is only revealed on the quantum level. In this review we consider the scale dependence of local gauge invariant operators and high-energy (Regge) behavior of scattering amplitudes to explain that the effective QCD dynamics in both cases is described by completely integrable systems that prove to be related to the celebrated Heisenberg spin chain and its generalizations.