the condition $(h''(\tilde t_0) + \frac{3}{4 \tilde t_0^2}) <0$ in (\[scalarpot2\]) leads to an AdS minimum. The correction term in the Kähler potential is chosen as

$$\label{Kahlercorrect}
h(\tilde T + \tilde T^*) \equiv 
-\frac{\alpha}{(\tilde T+\tilde T^*)} - \alpha_1 (\tilde T + \tilde T^*)^2,$$

where $\alpha$ and $\alpha_1$ are two independent parameters. It is noteworthy that in (\[Kahlercorrect\]) appropriate choice of parameters $\alpha$ and $\alpha_1$ may produce the dS vacuum as well. However in this particular context only the nature of AdS vacua is studied.

The function $f(\tilde{s})$ is chosen to be, $$\label{fs}
f(\tilde{s}) = m^3((\ln{\tilde{s}})^2 + k \ln{\tilde{s}} + k_1 \tilde{s}),$$

where $k$ and $k_1$ are free parameters and $m$ is the scale of the potential. For this choice the superpotential corresponding to the moduli field $T$ at the VEV becomes,

$$\label{superpotVEV}
W^{T}=\frac{A a e^{-a \tilde t_0}}{-\frac{3}{2 \tilde t_0}+\frac{\alpha}{4 \tilde t_0 ^2 } - 4\alpha_1 \tilde{t}_0}.$$

Furthermore the constraint (\[const2\]) acquires the form,

$$\begin{split}
\label{const3}
&(1+\sqrt{3})\left[\frac{A a e^{-a \tilde t_0}}{-\frac{3}{2 \tilde t_0}+\frac{\alpha}{4 \tilde t_0 ^2 } - 
4\alpha_1 \tilde{t}_0 }+ m^3 ((\ln{\tilde{s}_0})^2 + k \ln{\tilde{s}_0} + k_1 \tilde{s}_0) 
\right]\\
&= 2\tilde s_0 m^3 \left(\frac {2 \ln{\tilde{s}_0}} {\tilde s_0} + \frac{k}{\tilde s_0}
+ k_1\right) . 
\end{split}$$

The VEV of the scalar 