Non-perturbative scalar potential inspired by type IIA strings on rigid CY

Abstract

International audienceMotivated by a class of flux compactifications of type IIA strings on rigid Calabi-Yau manifolds, preserving N=2 local supersymmetry in four dimensions, we derive a non-perturbative potential of all scalar fields from the exact D-instanton corrected metric on the hypermultiplet moduli space. Applying this potential to moduli stabilization, we find a discrete set of exact vacua for axions. At these critical points, the stability problem is decoupled into two subspaces spanned by the axions and the other fields (dilaton and Kähler moduli), respectively. Whereas the stability of the axions is easily achieved, numerical analysis shows instabilities in the second subspace

No inflation in type IIA strings on rigid Calabi–Yau spaces

“…Such manifold has the vanishing Hodge number h 2,1 (Y) = 0, so that the LEEA is described by N = 2 supergravity interacting with the so-called universal hypermultiplet (UH), and some number h 1,1 (Y) > 0 of vector multiplets. As was found in [17], this class of N = 2 compactifications does not allow meta-stable vacua, within validity of the approximation used. However, it is still has to be checked whether the same scalar potential is suitable for slow roll inflation.…”

“…Our results extend the applicability of the "no-go" statement [14], ruling out slow roll inflation in type IIA/CY strings, beyond the semi-classical approximation in the case of rigid CY. The absence of viable inflation in type IIA strings on rigid CY with N = 2 supersymmetry in four dimensions is also related to the absence of meta-stable vacua found in [17] for a limited range of the string coupling values, but including all D-instanton corrections.…”

“…The other h 1,1 independent combinations of these fields enter the potential only via instanton corrections. This shows that the instanton corrections are indispensable for axion stabilization, and allow a simple solution [17],…”

“…The charge vectors corresponding to our choice of fluxes and generating the isometries of the metric (8) are given by [17]…”

“…Our paper is organized as follows. In the next section 2 we review basic information about the relevant CY string compactifications with fluxes, and provide the scalar potential in the corresponding (gauged) N = 2 supergravity by following [17] that is our starting point. In section 3 we study the perturbative scalar potential and slow roll conditions.…”