  We systematically study supersymmetric embeddings of D-brane probes of
different dimensionality in the AdS_5xY^{p,q} background of type IIB string
theory. The main technique employed is the kappa symmetry of the probe's
worldvolume theory. In the case of D3-branes, we recover the known three-cycles
dual to the dibaryonic operators of the gauge theory and we also find a new
family of supersymmetric embeddings. The BPS fluctuations of dibaryons are
analyzed and shown to match the gauge theory results. Supersymmetric
configurations of D5-branes, representing domain walls, and of spacetime
filling D7-branes (which can be used to add flavor) are also found. We also
study the baryon vertex and some other embeddings which break supersymmetry but
are nevertheless stable.
