Type IIA flux vacua with mobile D6-branes and alpha'-corrections

Type IIA flux compactifications have proven to be a rich framework to construct phenomenologically appealing string vacua. However, a better understanding of such a flux landscape in the presence of D-branes is required if one wants to find realistic vacuum solutions. In this thesis, we study perturbative Type IIA flux vacua with an underlying Calabi-Yau geometry, by mean of the flux-axion polynomial formalism.

In a first stage, we consider type IIA Calabi-Yau orientifolds with background fluxes and rewrite the classical flux potential as a bilinear of flux-axion polynomials invariant under the discrete shift symmetries of the compactification. We perform a systematic search of purely closed string vacua, showing that one can easily rewrite the conditions for N = 0 Minkowski and N = 1 AdS in terms of simple algebraic equations on the axion polynomials. Then we turn to the search of vacua in compactifications with fluxes and mobile D6-branes. The presence of D6-brane moduli redefines the four-dimensional dilaton and complex structure moduli and simultaneously destroy the nice factorization between Kähler and complex structure moduli in the Kähler potential, complicating the search of vacua in terms of the effective Kähler potential and superpotential. Nevertheless, one may still express the F-term scalar potential as a bilinear of such polynomials, which allows us to find a new and more general class of N = 0 Minkowski vacua, which present a quite simple structure of contravariant F-terms. We compute the set of soft supersymmetry breaking terms for chiral models of intersecting D6-branes in such vacua, finding a quite universal pattern.

In a second stage, we further study type IIA Calabi-Yau flux compactifications with perturbative α′-corrections. It is a well-known fact that the inclusion of such alpha′- corrections allows to construct the mirror duals of type IIB Calabi-Yau flux compactifications, in which the effect of flux backreaction is under control. We compute the alpha′-corrected scalar potential generated by RR and NS fluxes, and reformulate it as a bilinear of the flux-axion polynomials. The use of such invariants allows to express in a compact and simple way the conditions for N = 0 Minkowski and N = 1 AdS flux vacua, and to extract the effect of α′-corrections on them.