justified in the following sections. However admitting such large value for $A \sim 10^{42}~\rm GeV^3$, the condition (\[const2\]) can only be satisfied if $f'(\tilde s)|_{VEV} \sim A >> f(\tilde s)|_{VEV}$ holds.

Extremization
=============

In this section the issue of the stability of the scalar potential (\[scalarpot\]) is addressed. The potential is required to satisfy the conditions for global minimum with well-defined VEV for all the fields. In this section the conditions for extremum for (\[scalarpot\]) are determined for arbitrary $f(\tilde{s})$ and $h(\tilde{t})$ where the constraints (\[constraint1\]) and (\[const2\]) have been used.

The first derivative of (\[scalarpot\]) with respect to the moduli $\tilde s$ yields the condition, $$\label{potmint1}
\begin{split}
\frac{\partial V_h}{\partial \tilde s}|_{\tilde s_0,\tilde t_0} =
& \frac{1}{16 \tilde s_0^2 \tilde t_0^3(3+4 \tilde t_0^2 h''[\tilde t_0])} 
[(2-\sqrt{3}) e^{h[\tilde t_0]}(4 \tilde s_0^2 f'[\tilde s_0](-\sqrt{3}f'[\tilde s_0]+(3+\sqrt{3} \tilde s_0 f''[\tilde s_0])\\
&(3+4 \tilde t_0^2 h''[\tilde t_0]) - (2+\sqrt{3})f[\tilde s_0]^2
(3+4 \tilde t_0 (h'[\tilde t_0](-3 + \tilde t_0 h'[\tilde t_0])-2 \tilde t_0 h''[\tilde t_0]))\\ 
&+2 \tilde s_0 f[\tilde s_0] (-2(2+\sqrt{3}) \tilde s_0 f''[\tilde s_0] 
(3+4 \tilde t_0^2 h''[\tilde t_0]) + f'[\tilde s_0] (12 +9 \sqrt{3} +h[\tilde t_0]\\
&+(-3(2+\sqrt{3})h'[\tilde t_0] + (2+\sqrt{3})\tilde t_0 h'[\tilde t_0]^2 -2 \tilde t_0 h'[\tilde t_0] ))))] = 0
\end{split}$$ Similarly the 