Supersymmetric nonlinear sigma model in AdS5

We construct the supersymmetric nonlinear sigma model in a fixed AdS₅ background. We use component fields and find that the complex bosons must be the coordinates of a hyper-Kähler manifold that admits a Killing vector satisfying an inhomogeneous tri-holomorphic condition. We propose boundary conditions that map the on-shell bulk hypermultiplets into off-shell chiral multiplets on 3-branes that foliate the bulk. The supersymmetric AdS₅ isometries reduce to superconformal transformations on the brane fields.