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

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.