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

TL;DR

This paper explores the strong coupling limit of large-$N$ QCD, reformulating it as constrained spin chains, analyzing their integrability properties, and estimating the roughening transition point.

Contribution

It introduces a spin chain reformulation of large-$N$ QCD at strong coupling and analyzes the integrability and constraints affecting these models.

Findings

Large class of integrable subsectors identified

Full spin chain is not integrable due to zigzag constraints

Roughening transition point estimated from subsector analysis

Abstract

We study the strong coupling expansion of large $N$ QCD in various dimensions, reformulating the Kogut-Susskind Hamiltonian on a square lattice in terms of (constrained) one dimensional spin chain models. We study the integrability properties of the spin chain obtained this way: there is large class of integrable subsectors, but we show that the full spin chain is not integrable, at least when viewed from a description based on Bethe ansatz. We demonstrate that the spin chains no longer possess integrability due to the constraints arising from the zigzag symmetry of the confining strings. The spin chain description properly estimates the roughening transition point by extrapolating the first-order analytical results based on integrability of some subsectors. The generalization to higher dimensions are also considered, where we also find the small subsectors without the zigzag constraints to be integrable.