String Integrability on the Coulomb Branch

The Coulomb branch of the N = 4 super-Yang-Mills theory is described by a D3-brane in the bulk of AdS_5 x S^5. We show that boundary conditions on this D3-brane preserve integrability of the AdS string. For that matter we construct dynamical and spectral parameter dependent reflection matrix that encodes an infinite number of conserved charges on the worldsheet of an open string ending on the D-brane.