its size. Identifying the two columns of the Young diagrams with the two threebranes, the number of boxes in each column determines the angular momentum and hence the size of each threebrane. In the limit that $N-b_0=O(N)$, $b_0=O(N)$ and $b_1=O(\sqrt{N})$ we have non-maximal giants which are separated by a distance of $O(1)$ in string units. In this limit, we expect the dynamics to simplify. Indeed, the system should be described by two $D3$ brane giant gravitons with open strings stretching between then. The action of the dilatation operator becomes $$DO_A(b_0,b_1) =g_{YM}^2\left(N-b_0\right)\times O\left({1\over b_1}\right)$$ $$\begin{aligned}
\nonumber
DO_B(b_0,b_1) =&&-{4\over 3}g_{YM}^2\left(N-b_0\right)\left[
O_B(b_0+1,b_1-2)-2\,O_B(b_0,b_1) + O_B(b_0-1,b_1+2) \right]\cr
&&+{2\sqrt {2}\over 3}g_{YM}^2\left(N-b_0\right)\left[O_C(b_0+1,b_1-2)
-2O_C(b_0+1,b_1)+O_C(b_0-1,b_1+2)\right]\end{aligned}$$ $$\begin{aligned}
\nonumber
DO_C(b_0,b_1) =&&{2\sqrt {2}\over 3}g_{YM}^2(N-b_0)\left[
 O_B(b_0+1,b_1-2)-2O_B(b_0,b_1)+O_B(b_0-1,b_1+2)\right]\cr
&&-{2\over 3}g_{YM}^2(N-b_0)\left[ O_C(b_0+1,b_1-2)-2O_C(b_0,b_1)+O_C(b_0-1,b_1+2)\right]\end{aligned}$$ $$\begin{aligned}
\nonumber
DO_D(b_0,b_1) =&&-{4\over 3}g_{YM}^2(N-b_0)\left[
O_D(b_0+1,b_1-2)-2O_D(b_0,b_1)+O_D(b_0-1,b_1+2)\right]\cr
&&+{2\sqrt {2}\over 3}g_{YM}^2(N-b_0)\left[
O_E(b_0+1,b_1-2)-2O_E(b_0,b_1)+O_E(b_0-1,b_1+2)\right]\end{aligned}$$ $$\begin{aligned}
\nonumber
DO_E(b_0,b_1) = &&{2\sqrt {2}\over 3}g_{YM}^2(N-b_0)\left[
O_D(b_0+1,b_1-2)-2O_D(b_0,b_1)+O_D(b_0-1,b_1+2)\right]\cr
&&-{2\over 3}g_{YM}^2(N-b_0)\left[
O_E(b_0+1,b_1-2)-2O_E(b_0,b_1)+O_E(b_0-1,b_1+2)\right]\end{aligned}$$ $$DO_F(b_0,b_1) =g_{YM}^2\left(N-b_0\right)\times O\left({1\over b_1}\right)$$ These results have a natural interpretation. Notice that there are four operators for which the $S_m$ representation is the totally antisymmetric representation. We will see that there are also four operators for which the corresponding states remain supersymmetric; this agreement between the number of operators for which the $S_m$ representation is the totally antisymmetric representation and the number of 