Type IIA flux vacua and -corrections

We analyse type IIA Calabi-Yau orientifolds with background fluxes, taking into account the effect of perturbative -corrections. In particular, we consider the corrections that modify the metrics in the Kahler sector of the compactification. As it has been argued in the literature, including such -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 -corrected scalar potential generated by the presence of RR and NS fluxes, and reformulate it as a bilinear of the flux-axion polynomials invariant under the discrete shift symmetries of the compactification. The use of such invariants allows to express in a compact and simple manner the conditions for Minkowski and AdS flux vacua, and to extract the effect of -corrections on them.