are nine possible operators that we can define $$\chi_A(b_0,b_1)=\chi_{\tiny \yng(2,2,2,2,2,2,1,1,1,1,1)\, \yng(2,2,2,2,2,2,1)\, \yng(1,1,1,1)}(Z,Y)
\qquad
\chi_B(b_0,b_1)=\chi_{\tiny \yng(2,2,2,2,2,2,1,1,1,1,1)\, \yng(2,2,2,2,2,1,1,1)\, \yng(1,1,1,1)}(Z,Y)$$ $$\chi_C(b_0,b_1)=\chi_{\tiny \yng(2,2,2,2,2,2,1,1,1,1,1)\,\yng(2,2,2,2,2,1,1,1)\, \yng(2,1,1)}(Z,Y)
\qquad
\chi_D(b_0,b_1)=\chi_{\tiny \yng(2,2,2,2,2,2,1,1,1,1,1)\, \yng(2,2,2,2,1,1,1,1,1)\, \yng(1,1,1,1)}(Z,Y)$$ $$\chi_E(b_0,b_1)=\chi_{\tiny \yng(2,2,2,2,2,2,1,1,1,1,1)\, \yng(2,2,2,2,1,1,1,1,1)\, \yng(2,1,1)}(Z,Y)
\qquad
\chi_F(b_0,b_1)=\chi_{\tiny \yng(2,2,2,2,2,2,1,1,1,1,1)\, \yng(2,2,2,2,1,1,1,1,1)\, \yng(2,2)}(Z,Y)$$ $$\chi_G(b_0,b_1)=\chi_{\tiny \yng(2,2,2,2,2,2,1,1,1,1,1)\, \yng(2,2,2,1,1,1,1,1,1,1)\, \yng(1,1,1,1)}(Z,Y)
\qquad
\chi_H(b_0,b_1)=\chi_{\tiny \yng(2,2,2,2,2,2,1,1,1,1,1)\, \yng(2,2,2,1,1,1,1,1,1,1)\, \yng(2,1,1)}(Z,Y)$$ $$\chi_I(b_0,b_1)=\chi_{\tiny \yng(2,2,2,2,2,2,1,1,1,1,1)\, \yng(2,2,1,1,1,1,1,1,1,1,1)\, \yng(1,1,1,1)}(Z,Y)$$ Again, the corresponding normalized operators are denoted using the capital letter $O$. The action of the dilatation operator is given in Appendix A.

In the limit that $N-b_0=O(N)$, $b_0=O(N)$ and $b_1=O(\sqrt{N})$ the dynamics again simplifies. The action of the dilatation operator becomes $$DO_A(b_0,b_1)=(N-b_0)g_{YM}^2\times O\left({1\over b_1}\right)$$ $$\begin{aligned}
\nonumber
DO_B(b_0,b_1) =&&-{3\over 2}g_{YM}^2\left(N-b_0\right)\left[
O_B(b_0+1,b_1-2)-2\,O_B(b_0,b_1) + O_B(b_0-1,b_1+2) \right]\cr
&&+{\sqrt {3}\over 2}g_{YM}^2\left(N-b_0\right)\left[O_C(b_0+1,b_1-2)
-2O_C(b_0+1,b_1)+O_C(b_0-1,b_1+2)\right]\end{aligned}$$ $$\begin{aligned}
\nonumber
DO_C(b_0,b_1) =&&{\sqrt {3}\over 2}g_{YM}^2(N-b_0)\left[
 O_B(b_0+1,b_1-2)-2O_B(b_0,b_1)+O_B(b_0-1,b_1+2)\right]\cr
&&-{1\over 2}g_{YM}^2(N-b_0)\left[ O_C(b_0+1,b_1-2)-2O_C(b_0,b_1)+O_C(b_0-1,b_1+2)\right]\end{aligned}$$ $$\begin{aligned}
\nonumber
DO_D(b_0,b_1) =&&-2g_{YM}^2\left(N-b_0\right)\left[
O_D(b_0+1,b_1-2)-2\,O_D(b_0,b_1) + O_D(b_0-1,b_1+2) \right]\cr
&&+{2\over \sqrt{3}}g_{YM}^2\left(N-b_0\right)\left[O_E(b_0+1,b_1-2)
-2O_E(b_0+1,b_1)+O_E(b_0-1,b_1+2)\right]\end{aligned}$$ $$\begin{aligned}
\nonumber
DO_E(b_0,b_1) =&&-2g_{YM}^2(N-b_0)\left[
 O_E(b_0+1,b_1-2)-2O_E(b_0,b_1)+O_E(b_0-1,b_1+2)\right]\cr
&&+{2\over \sqrt{3}}g_{YM}^2(N-b_0)\left[ O_D(b_0+1,b_1-2)-2O_D(b_0,b_1)+O_D(b_0-1,b_1+2)\right]\cr
&&+{2\sqrt{6}\over 3}g_{YM}^2(N-b_0)\left[ O_F(b_0+1,b_1-2)-2O_F(b_0,b_1)+O_F(b_0-1,b_1+2)\right]\end{aligned}$$ $$\begin{aligned}
\nonumber
DO_F(b_0,b_1) =&&-2g_{YM}^2\left(N-b_0\right)\left[
O_F(b_0+1,b_1-2)-2\,O_F(b_0,b_1) + O_F(b_0-1,b_1+2) \right]\cr
&&+{2\sqrt{6}\over 3}g_{YM}^2\left(N-b_0\right)\left[O_E(b_0+1,b_1-2)
-2O_E(b_0+1,b_1)+O_E(b_0-1,b_1+2)\right]\end{aligned}$$ $$\begin{aligned}
\nonumber
DO_G(b_0,b_1) =&&-{3\over 2}g_{YM}^2\left(N-b_0\right)\left[
O_G(b_0+1,b_1-2)-2\,O_G(b_0,b_1) + O_G(b_0-1,b_1+2) \right]\cr
&&+{\sqrt{3}\over 2}g_{YM}^2\left(N-b_0\right)\left[O_H(b_0+1,b_1-2)
-2O_H(b_0+1,b_1)+O_H(b_0-1,b_1+2)\right]\end{aligned}$$ $$\begin{aligned}
\nonumber
DO_H(b_0,b_1) =&&-{1\over 2}g_{YM}^2\left(N-b_0\right)\left[
O_H(b_0+1,b_1-2)-2\,O_H(b_0,b_1) + O_H(b_0-1,b_1+2) \right]\cr
&&+{\sqrt{3}\over 2}g_{YM}^2\left(N-b_0\right)\left[O_G(b_0+1,b_1-2)
-2O_G(b_0+1,b_1)+O_G(b_0-1,b_1+2)\right]\end{aligned}$$ $$DO_I(b_0,b_1)=(N-b_0)g_{YM}^2\times O\left({1\over b_1}\right)$$ We can again identify combinations of operators that are annihilated by $D$, that is, that are BPS. Apart from $O_A(b_0,b_1)$ and $O_I(b_0,b_1)$ we have $O_B(b_0,b_1)+\sqrt{3}O_C(b_0,b_1)$, 