Integrable Spin Chains from large-$N$ QCD at strong coupling

TL;DR

This paper demonstrates that certain spin chains derived from large-N QCD at strong coupling are integrable, revealing new solvable models in the context of confining strings and lattice gauge theories.

Contribution

It shows that the full spin chain associated with large-N QCD is integrable in arbitrary dimensions when a relaxed zigzag symmetry constraint is applied.

Findings

Subsectors of the spin chain are integrable.

Full spin chain becomes integrable with relaxed zigzag symmetry.

Integrability holds in arbitrary dimensions.

Abstract

We study a spin chain for a confining string that arises at first order in degenerate perturbation from the strong-coupling expansion of the Kogut-Susskind Hamiltonian on a square lattice in the leading large $N$ expansion. We show some subsectors are integrable and that with a relaxed constraint related to zigzag symmetry, the full spin chain is integrable in arbitrary dimensions.