String integrability of the ABJM defect

ABJM theory in the presence of a half-BPS domain wall is dual to D2-D4 probe brane system with nonzero worldvolume flux. The was recently shown be integrable lowest order perturbation and bond dimension. In present paper we show that string this integrable, namely boundary conditions on D4-brane preserve integrability Green-Schwarz sigma model. Our result suggests all loop orders for any value