$$\mathcal M= \left(\begin{array}{cc} -m\square^{1/2}P_{-} & \square
(P_2+\xi(P_1+P_T))\\ \square (P_1+\xi(P_2+P_T)) &
-m\square^{1/2}P_{+}
\end{array} \right) ,\label{M}$$ with $$P_+ = \frac{D^2}{4\Box^{1/2}}, \quad  
P_- = \frac{{\bar D}^2}{4\Box^{1/2}}. \label{P+}$$ The interaction matrix ${\cal V}$ is $${\mathcal V}=\left(\begin{array}{cc} F & 0\\ 0 &
\bar{F}\end{array}\right) .\label{V}$$ There are two types of elements in $\cal{V}$, local and nonlocal. We split them into $F_1$ and $F_2$ $$F(z,z')=F_{1}(z)\delta(z-z')+F_{2}(z,z'). \label{Fzz'}$$ Elements of $F_1$ are given by $$\begin{aligned}
F_{1} (z)&=& \sum_{i=0}^{10} F^{(i)}\nonumber\\
&=& -\frac{\lambda}{2} \Phi \bar{D}^2 -\frac{\lambda}{48}
K^{m}_{\ a}K^{*na} \overleftarrow{\bar{D}^{2} D^{\alpha}}
(\partial_{m}\Phi) \theta\theta\bar{\theta}\bar{\theta}
\partial_{n}D_{\alpha}\bar{D}^{2}\nonumber \\ 
&& - \frac{\lambda}{48} K^{m}_{\ a}K^{*na}
\overleftarrow{\bar{D}^{2} D^{\alpha}}
(\partial_{m}D_{\alpha}\Phi) \theta\theta\bar{\theta}\bar{\theta}
\partial_{n}\bar{D}^{2}\nonumber\\
&& - \frac{\lambda}{48} K^{m}_{\ a}K^{*na} \overleftarrow{\partial_{m}\bar{D}^{2}}
(D^{\alpha}\Phi) \theta\theta\bar{\theta}\bar{\theta}
\partial_{n}D_{\alpha}\bar{D}^{2} \nonumber\\
&&+\frac{\lambda}{24} K^{m}_{\ a}K^{*n}_{\ b}
\overleftarrow{\bar{D}^{2}D^{\alpha}}(\sigma^{ab})_{\alpha}^{\
\beta}(\partial_{m}\Phi)\theta\theta\bar{\theta}\bar{\theta}
\partial_{n} D_{\beta} \bar{D}^{2} \nonumber\\ & &+\frac{\lambda}{24} K^{m}_{\ a}K^{*n}_{\ b}
\overleftarrow{\partial_{m}\bar{D}^{2}}(D^{\alpha}\Phi)(\sigma^{ab})_{\alpha}^{\
\beta}\theta\theta\bar{\theta}\bar{\theta}
\partial_{n} D_{\beta} \bar{D}^{2} \nonumber\\ 
&&+\frac{\lambda}{24} K^{m}_{\ a}K^{*n}_{\ b}
\overleftarrow{\partial_{m}\bar{D}^{2}}(\partial_{n}D^{\alpha}\Phi)(\sigma^{ba})_{\alpha}^{\
\beta}\theta\theta\bar{\theta}\bar{\theta} D_{\beta} \bar{D}^{2}
\nonumber\\ 
&& -\frac{\lambda}{512} K^{mn}K_{mn}
\overleftarrow{\bar{D}^{2}D^{2}} \Phi \bar{\theta}\bar{\theta}
D^{2}\bar{D}^{2} \label{F1} \\ 
&& -\frac{\lambda}{96} K^{m}_{\
a}K^{*na} \overleftarrow{\partial_{m}\bar{D}^2} (\partial_{n}\Phi)
\theta\theta\bar{\theta}\bar{\theta} D^{2}\bar{D}^2 \nonumber\\ 
&& -\frac{\lambda}{192}K^{m}_{\ a}K^{*na}
\overleftarrow{\partial_{m}\bar{D}^{2}}
(D^{2}\Phi)\theta\theta\bar{\theta}\bar{\theta}
\partial_{n}\bar{D}^2\nonumber\\ 
&& +\frac{\lambda}{96} K^{m}_{\ a}K^{*na}
\overleftarrow{\square\bar{D}^{2}} \Big(\int {\mbox{d}}^8 z'\hspace{1mm}
(\partial_{m}D^{2}\Phi)(z') \frac{1}{\Box_{z'}}\delta(z'-z)\Big)
\theta\theta\bar{\theta}\bar{\theta}
\partial_{n}\bar{D}^2, \nonumber\end{aligned}$$ while the elements of $F_2$ read $$\begin{aligned}
F_{2}(z,z') &=& \sum_{i=11}^{12} F^{(i)}\nonumber\\
&=& \frac{\lambda}{96} K^{m}_{\ a}K^{*na}
\overleftarrow{\partial_{m}\bar{D}^{2} D^{2}} 
\frac{1}{\Box_{z'}}\delta(z'-z)\theta\theta\bar{\theta}\bar{\theta}
((\partial_{n}\Phi)\square\bar{D}^{2})(z')
\nonumber\\ 
&& + \frac{\lambda}{96} K^{m}_{\ a}K^{*na}
\overleftarrow{\partial_{m}\bar{D}^{2} D^{2}} 
\frac{1}{\Box_{z'}}\delta(z'-z)\theta\theta\bar{\theta}\bar{\theta}
(\Box\Phi \partial_{n}\bar{D}^{2})(z') 