Open Spin Chains in Super Yang-Mills at Higher Loops: Some Potential Problems with Integrability

TL;DR

This paper investigates the behavior of open quantum spin chains in super Yang-Mills theory at higher loops, revealing potential issues with integrability beyond the one-loop order, which impacts understanding of dual string states.

Contribution

It explicitly constructs the two-loop open spin chain for non-BPS giant gravitons and analyzes the potential breakdown of integrability at higher loops.

Findings

Open spin chain constructed at two loops for non-BPS giant gravitons.

Integrability holds at one loop but may break down at two and higher loops.

Uses coordinate Bethe ansatz to analyze integrability.

Abstract

The super Yang-Mills duals of open strings attached to maximal giant gravitons are studied in perturbation theory. It is shown that non-BPS baryonic excitations of the gauge theory can be studied within the paradigm of open quantum spin chains even beyond the leading order in perturbation theory. The open spin chain describing the two loop mixing of non-BPS giant gravitons charged under an su(2) of the so(6) R symmetry group is explicitly constructed. It is also shown that although the corresponding open spin chain is integrable at the one loop order, there is a potential breakdown of integrability at two and higher loops. The study of integrability is performed using coordinate Bethe ansatz techniques.