Chiral Integrable Boundary States in the SU(4) Alternating Spin Chain

TL;DR

This paper discovers the first chiral integrable boundary states in the SU(4) alternating spin chain, expanding understanding of boundary states in integrable models relevant to ABJM theory.

Contribution

It identifies specific chiral boundary states in the SU(4) spin chain using a new integrability condition, which were previously thought to be absent.

Findings

Identification of two-site and four-site chiral boundary states.

Numerical evidence suggests other basis states are not chiral integrable.

Computed overlaps between boundary states and Bethe eigenstates.

Abstract

Previously identified integrable boundary states in ABJM theory are exclusively achiral. This paper presents the first chiral integrable boundary states in the $SU(4)$ alternating spin chain from the planar two-loop dilatation operator in the scalar sector. Utilizing a sufficient condition for the untwisted integrable condition, we identify specific two-site and four-site basis boundary states as chiral integrable states. Numerical evidence indicates that other basis states are unlikely to be chiral integrable. Furthermore, we compute the overlaps between these chiral integrable basis states and on-shell Bethe eigenstates.