  We study the one-loop anomalous dimensions of operators in the ${\cal N}=4$
super Yang-Mills theory that are dual to open strings ending on giant
gravitons. We consider both AdS and sphere giants as well as boundstates of
them. The open strings we consider carry angular momentum on an S^3 embedded in
the S^5 of the AdS$_5\times$S^5 background. The main result of this article is
that we derive a bosonic lattice Hamiltonian that describes the one loop mixing
of the operators dual to the general excited giant graviton system. A
semiclassical analysis of the Hamiltonian allows us to give a geometrical
interpretation for the labeling used to describe the gauge theory operators. We
also argue that AdS giant gravitons are unstable against the excitations
considered.
