One-Loop QCD Spin Chain and its Spectrum

TL;DR

This paper analyzes the renormalization of gauge invariant operators in large Nc QCD, revealing an integrable spin chain sector with specific gluonic operators and their excitation spectra.

Contribution

It introduces a large integrable sector in large Nc QCD related to gluonic operators and characterizes its spectrum and ground state.

Findings

Identifies an integrable spin chain sector in large Nc QCD

Characterizes the ground state as an anti-ferromagnetic XXX1 spin chain

Describes excitations with relativistic and non-relativistic dispersion relations

Abstract

We study the renormalization of gauge invariant operators in large Nc QCD. We compute the complete matrix of anomalous dimensions to leading order in the 't Hooft coupling and study its eigenvalues. Thinking of the mixing matrix as the Hamiltonian of a generalized spin chain we find a large integrable sector consisting of purely gluonic operators constructed with self-dual field strengths and an arbitrary number of derivatives. This sector contains the true ground state of the spin chain and all the gapless excitations above it. The ground state is essentially the anti-ferromagnetic ground state of a XXX1 spin chain and the excitations carry either a chiral spin quantum number with relativistic dispersion relation or an anti-chiral one with non-relativistic dispersion relation.