Type IIA flux vacua and α ′-corrections

We analyse type IIA Calabi-Yau orientifolds with background fluxes, taking into account the effect of perturbative α-corrections. In particular, we consider the α corrections that modify the metrics in the Kähler sector of the compactification. As it has been argued in the literature, including such α-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 α-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 α-corrections on them.This work is supported by the Spanish Research Agency (Agencia Estatal de Investi-gación) through the grant IFT Centro de Excelencia Severo Ochoa SEV-2016-0597, by the grant FPA2015-65480-P from MINECO/FEDER EU, by the grant IJCI-2015-24908 from MINECO, and by the ERC Advanced Grant SPLE under contract ERC-2012-ADG-20120216-320421. D.E. is supported through the FPI grant SVP-2014-068283