Stabilising all K\"ahler moduli in perturbative LVS

In this work we investigate the moduli stabilisation problem and the requirements for de Sitter vacua within the framework of type IIB string theory. Using perturbative effects arising from the various sources such as $\alpha^\prime$ corrections, logarithmic as well as KK and winding-type string-loop corrections along with the higher derivative $F^4$-contributions, we present a moduli stabilisation scheme in which the overall volume is realised at exponentially large values such that $\langle {\cal V} \rangle \simeq e^{a/g_s^2}$ in the weak coupling regime, where $a$ is a parameter given as $a = \frac{\zeta[3]}{2 \zeta[2]} \simeq 0.365381$. We also present a concrete global construction using a $K3$-fibred CY threefold with $h^{1,1} =3$ which shares many of its properties with those of the standard toroidal case, and subsequently generates the appropriate corrections needed to fix all the three K\"ahler moduli at the perturbative level. We further discuss whether de Sitter vacua can be ensured through appropriate contributions of uplifting terms in the effective potential.