  We study the one-loop anomalous dimensions of the Super Yang-Mills dual
operators to open strings ending on AdS giant gravitons. AdS giant gravitons
have no upper bound for their angular momentum and we represent them by the
contraction of scalar fields, carrying the appropriate R-charge, with a totally
symmetric tensor. We represent the open string motion along AdS directions by
appending to the giant graviton operator a product of fields including
covariant derivatives. We derive a bosonic lattice Hamiltonian that describes
the mixing of these excited AdS giants operators under the action of the
one-loop dilatation operator of N=4 SYM. This Hamiltonian captures several
intuitive differences with respect to the case of sphere giant gravitons. A
semiclassical analysis of the Hamiltonian allows us to give a geometrical
interpretation for the labeling used to describe the fields products appended
to the AdS giant operators. It also allows us to show evidence for the
existence of continuous bands in the Hamiltonian spectrum.
