three Young diagrams labeling the restricted Schur polynomial. The second Young diagram, $r$, (which specifies an irreducible representation of $S_n$) is specified by stating the number of rows with two boxes ($=b_0$) and the number of rows with a single box ($=b_1$). The third Young diagram label, $s$, (which specifies an irreducible representation of $S_3$) and the first Young diagram label, $R$, (which specifies an irreducible representation of $S_{n+3}$) can now be built from $r$ by specifying which boxes in $R$ are to be removed to obtain $r$ and how these boxes are to be organized into an $S_3$ irreducible representation. There are 6 possibilities $$\chi_A(b_0,b_1)=\chi_{\tiny \yng(2,2,2,2,2,1,1,1,1,1)\,\yng(2,2,2,2,2,1,1)\,\yng(1,1,1)}(Z,Y)
\qquad
\chi_B(b_0,b_1)=\chi_{\tiny \yng(2,2,2,2,2,1,1,1,1,1)\,\yng(2,2,2,2,1,1,1,1)\,\yng(1,1,1)}(Z,Y)$$ $$\chi_C(b_0,b_1)=\chi_{\tiny \yng(2,2,2,2,2,1,1,1,1,1)\,\yng(2,2,2,2,1,1,1,1)\,\yng(2,1)}(Z,Y)
\qquad
\chi_D(b_0,b_1)=\chi_{\tiny \yng(2,2,2,2,2,1,1,1,1,1)\,\yng(2,2,2,1,1,1,1,1,1)\,\yng(1,1,1)}(Z,Y)$$ $$\chi_E(b_0,b_1)=\chi_{\tiny \yng(2,2,2,2,2,1,1,1,1,1)\,\yng(2,2,2,1,1,1,1,1,1)\,\yng(2,1)}(Z,Y)
\qquad
\chi_F(b_0,b_1)=\chi_{\tiny \yng(2,2,2,2,2,1,1,1,1,1)\,\yng(2,2,1,1,1,1,1,1,1,1)\,\yng(1,1,1)}(Z,Y)$$ The corresponding normalized operators are denoted using the capital letter $O$. In view of the discussion of section 3, we know that $b_0$ is $O(N)$ and $b_1$ ranges from 0 or 1 to $O(N)$. The action of the dilatation operator is given in Appendix A.

The ${\cal R}$-charge of an operator in the field theory maps into the angular momentum of the dual string theory state. Thanks to the Myers effect[@Myers:1999ps] the angular momentum of the string theory state determines 