  We propose gauge theory operators built using a complex Matrix scalar which
are dual to brane-anti-brane systems in $AdS_5 \times S^5 $, in the zero
coupling limit of the dual Yang-Mills. The branes involved are half-BPS giant
gravitons. The proposed operators dual to giant-anti-giant configurations
satisfy the appropriate orthogonality properties. Projection operators in
Brauer algebras are used to construct the relevant multi-trace Matrix
operators. These are related to the ``coupled representations'' which appear in
2D Yang-Mills theory. We discuss the implications of these results for the
quantum mechanics of a complex matrix model, the counting of non-supersymmetric
operators and the physics of brane-anti-brane systems. The stringy exclusion
principle known from the properties of half-BPS giant gravitons, has a new
incarnation in this context. It involves a qualitative change in the map
between brane-anti-brane states to gauge theory operators. In the case of a
pair of sphere giant and anti-giant this change occurs when the sum of the
magnitudes of their angular momenta reaches $N$.
