The D3-D5 and D2-D4 probe-brane systems with nonzero worldvolume flux are holographically dual to N=4 super Yang-Mills and ABJM theoryin the presence of half-BPS domain walls. The two domain wallsystems are thought to be integrable; the evidence comes mainly from the studyof correlation functionsat weak coupling.
In the present talk we show that the string theory duals of these systems are classically integrable. In other words, the string boundary conditions on the probe branes preserve the integrability of the corresponding Green-Schwarz sigma models. This finding suggests that the dual domain wall systems are integrable to all loop orders and for any value of the bond dimension.
