New Integrable Structures in Large-N QCD

TL;DR

This paper uncovers integrable structures in large-N QCD by analyzing the anomalous dimensions of field strength operators, revealing a solvable spin chain model and a connection to the SU(2) WZW model.

Contribution

It introduces an integrable spin chain framework for large-N QCD operators and solves it exactly using Bethe ansatz, linking to conformal field theory.

Findings

The Hamiltonian for selfdual components is integrable.

Exact solutions are obtained via Bethe ansatz.

Continuum limit relates to SU(2) WZW model.

Abstract

We study the anomalous dimensions of single trace operators composed of field strengths $F_{\mu\nu}$ in large-N QCD. The matrix of anomalous dimensions is the Hamiltonian of a compact spin chain with two spin one representations at each vertex corresponding to the selfdual and anti-selfdual components of $F_{\mu\nu}$. Due to the special form of the interaction it is possible to study separately renormalization of purely selfdual components. In this sector the Hamiltonian is integrable and can be exactly solved by Bethe ansatz. Its continuum limit is described by the level two SU(2) WZW model.