Solving for the integrable boundary states of the ABJM spin chain from $KT$-relations

Nan Bai; Hui Yang; Mao-Zhong Shao

Solving for the integrable boundary states of the ABJM spin chain from $KT$-relations

High Energy Physics - Theory 2026-07-05 v1

Authors: Nan Bai , Hui Yang , Mao-Zhong Shao

Abstract

We study integrable boundary states of the alternating SU(4) spin chain arising in ABJM theory. Starting from the $KT$ -relation, we directly solve the integrability constraints for states with $n$ -site translational invariance. For odd and even $n$ , these constraints are reduced respectively to state equations and operator equations for the elementary $n$ -site block and the matrix $K(u)$ . We analyze chiral and achiral cases for $n\leq4$ . In the 1-site case we allow general operator-valued integrable pairs with an internal space, while in the remaining cases we focus on $c$ -number solutions.

Keywords

ABJM theory spin chain integrable boundary states KT-relation SU(4) translational invariance

Cite

@article{arxiv.2607.04203,
  title  = {Solving for the integrable boundary states of the ABJM spin chain from $KT$-relations},
  author = {Nan Bai and Hui Yang and Mao-Zhong Shao},
  journal= {arXiv preprint arXiv:2607.04203},
  year   = {2026}
}