Boundary bound states and integrable Wilson loops in ABJM

We derive an integrable reflection matrix for the scattering of excitations from a boundary with a degree of freedom when the reflection process preserves an $SU(1\mathrm{\mid }2)$ symmetry. As this residual symmetry is not sufficient to fully determine the reflection matrix, we use the boundary remnant of the Yangian symmetry invariance and obtain a family of integrable solutions. A concrete realization of this setup is found when studying insertions in the 1/2 BPS Wilson loop in ABJM theory. The boundary degree of freedom appears as a boundary bound state due to poles in the dressing phase of the reflection matrix. We also compare our results with those obtained from the boundary bound state bootstrap procedure. The ABJM Wilson loop example enables us to perform perturbative verifications of our results.