Fluxes, Vacua, and Tadpoles meet Landau-Ginzburg and Fermat

TL;DR

This paper explores flux vacua in Landau-Ginzburg models, revealing new supersymmetric solutions, analyzing their stability, and testing their consistency with swampland conjectures in string theory.

Contribution

It provides new infinite families of supersymmetric vacua and examines their properties in relation to the tadpole conjecture and swampland criteria.

Findings

Supersymmetric flux configurations at the Fermat point saturate the tadpole.

Not all massless fields are flat directions at higher order.

New infinite families of Minkowski and AdS vacua are described.

Abstract

Type IIB flux vacua based on Landau-Ginzburg models without K\"ahler deformations provide fully-controlled insights into the non-geometric and strongly-coupled string landscape. We show here that supersymmetric flux configurations at the Fermat point of the $1^9$ model, which were found long-time ago to saturate the orientifold tadpole, leave a number of massless fields, which however are not all flat directions of the superpotential at higher order. More generally, the rank of the Hessian of the superpotential is compatible with a suitably formulated tadpole conjecture for all fluxes that we found. Moreover, we describe new infinite families of supersymmetric 4d $\mathcal{N}=1$ Minkowski and AdS vacua and confront them with several other swampland conjectures.