}_I K$ is the Kähler metric. Now, using $F^M=M^3_p e^{G/2}K^{M \bar{P}} G_{\bar{P}}$ the scalar potential can be recast as

$$\label{pot2}
V(\phi_M,{\phi_M}^*)=\left(\bar{F}^{\bar{N}} K_{\bar{N} M} F^M-3 M_p^4 
e^{G}\right).$$

In type-IIB String theory de-Sitter solutions are forbidden in the leading order of $ \alpha' $ (the string tension) and $g_s$ (the string coupling) by a no-go theorem [@Maldacena]. So a natural way of finding a de-Sitter solution in string theory is to include corrections from higher order in $\alpha'$ and $g_s$ to the no-scale structure. In [@KKLT] this objective is achieved in a two fold way :

1.  In the presence of a non-zero flux the Calabi-Yau moduli combines suitably to form a superpotential of the form

    $$\label{Superpots}
     W = \int_M G_3 \wedge \Omega = \int_M (F_3 - \tau H_3) \Omega$$

    where $H_3$ and $F_3$ are the NS-NS and R-R three-form fluxes and $\tau$ is the axion-dilaton of type-IIB string theory. The Kähler structure of the internal manifold (Calabi-Yau four-fold) is encoded in a Kähler potential whose tree-level form is

    $$\label{Kahlers}
    { K} = M^2_p(-3 ln[- i (\rho - \overline{\rho})] - ln[- i 
    (\tau - \overline{\tau})] - ln [\int_M \Omega \wedge \overline{\Omega}]),$$

    where $\rho$ is the single volume modulus.

    This structure however does 