Moduli stabilisation for the dark dimension scenario

This thesis provides a moduli stabilisation mechanism for the Dark Dimension (DD) scenario within the framework of type IIB superstring theory. The DD scenario is a recent proposal which involves one large extra dimension with associated Kaluza-Klein (KK) scale around the cosmological constant scale, a tower of light sterile neutrinos and dark matter from massive KK gravitons. Realising a model with just one large extra dimension out of the six extra dimensions of string theory requires an anisotropic moduli stabilisation. This is achieved in the context of the type IIB Large Volume Scenario (LVS) which allows to obtain a low Kaluza-Klein scale thanks to the fact that the Calabi-Yau volume is exponentially large in string units. Anisotropy is realised by considering a Calabi-Yau threefold which is a K3 fibration over a P1 base. The volume of the K3 fibre is stabilised at relatively small values by perturbative corrections to the effective action, in particular string loops and higher derivative effects. This leaves an exponentially large volume of the 2-dimensional P1 base. Thanks to a hierarchical stabilisation of the complex structure moduli, one can then ensure that the P1 is deformed into an elongated cigar, leading to a model with just one large extra dimension. Interestingly, the desired anisotropy and low KK scale can be obtained for natural choices of the microscopic parameters.