  Giant gravitons in AdS_5 x S^5, and its orbifolds, have a dual field theory
representation as states created by chiral primary operators. We argue that
these operators are not single-trace operators in the conformal field theory,
but rather are determinants and subdeterminants of scalar fields; the stringy
exclusion principle applies to these operators. Evidence for this
identification comes from three sources: (a) topological considerations in
orbifolds, (b) computation of protected correlators using free field theory and
(c) a Matrix model argument. The last argument applies to AdS_7 x S^4 and the
dual (2,0) theory, where we use algebraic aspects of the fuzzy 4-sphere to
compute the expectation value of a giant graviton operator along the Coulomb
branch of the theory.
