Kähler potential we arrive at, $$\label{superpot4} 
     W=W_0 + A e^{- a \tilde{T}}~,~~~  K=-3 M_p^2 \log(\tilde{T} + 
    \tilde{T}^*),$$

    where $\tilde T=\frac{T}{M_p}$.\
    In a supersymmetric vacuum $D_T {W} = 0$. The axion field in $\rho$ is set to zero for the sake of simplification. $\{A, a, W_0\}$ is taken to be real and $W_0$ to be negative. The condition for susy preserving vacua corresponds to the minimum of the scalar potential determined by the VEV of $T$.

    $$D_T  W=0 \Longrightarrow W_0=-A e^{-a \tilde{t_0}}(1 + \frac{2}{3} a 
    \tilde{t_0})\label{condition}.$$

    Here $\tilde t_0$ denotes the VEV of $\tilde T$. This makes the scalar potential (\[pot1\]) negative at the minimum and can be given by,

    $$\label{adspot}
    V_{AdS}=-(3 e^{ K/M_p^2} {W}^2/M_p^2)_{AdS}={\frac{1}{M_p^2}}\frac{-a^2 A^2 e^{-2 a \tilde{t_0}}}
    {6 \tilde{t_0}}$$

    Thus a supersymmetry preserving AdS minimum has been generated. Fixing the values of $\{A,a, W_0\}$, one can estimate the VEV of the moduli $T$ via (\[condition\]) which in turn determines the $V_{AdS}$ through (\[adspot\]).

2.  The next important step is to add a de-Sitter lifting term to the scalar potential. The principal issue is to allow for generation of some extra energy from the flux background which shows up in the scalar potential as an extra term namely $D/T^3$. This 