# Type IIA Flux Vacua and $\alpha'$-corrections

## TL;DR

This paper investigates how perturbative $eta$-corrections influence the scalar potential and vacuum conditions in type IIA Calabi-Yau orientifold flux compactifications, providing a framework for understanding mirror duals of type IIB flux vacua.

## Contribution

It computes the $eta$-corrected scalar potential and reformulates it using flux-axion invariants, clarifying the impact of $eta$-corrections on flux vacua conditions.

## Key findings

- $eta$-corrections modify the scalar potential in flux compactifications.
- Invariants under discrete shift symmetries simplify the vacuum analysis.
- Conditions for Minkowski and AdS vacua are explicitly affected by $eta$-corrections.

## Abstract

We analyse type IIA Calabi-Yau orientifolds with backgroud fluxes, taking into account the effect of perturbative $\alpha'$-corrections. In particular, we consider the $\alpha'$-corrections that modify the metrics in the K\"ahler sector of the compactification. As it has been argued in the literature, including 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 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 $\alpha'$-corrections on them.