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A<sc>bstract</sc> Recent work on flux compactifications suggests that the tadpole constraint generically allows only a limited number of complex structure moduli to become massive, i.e., be stabilized at quadratic order in the spacetime superpotential. We study the effects of higher-order terms systematically around the Fermat point in the 1⁹Landau-Ginzburg model. This model lives at strong coupling and features no Kähler moduli. We show that indeed massless fields can be stabilized in this fashion. We observe that, depending on the flux, this mechanism is more effective when the number of initially massless fields is large. These findings are compatible with both the tadpole conjecture and the massless Minkowski conjecture. Along the way, we complete the classification of integral flux vectors with small tadpole contribution. Thereby we are closing in on a future complete understanding of all possible flux configurations in the 1⁹Landau-Ginzburg model. 

A bstract Type IIB flux vacua based on Landau-Ginzburg models without Kähler 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 $$ \mathcal{N} $$ N = 1 Minkowski and AdS vacua and confront them with several other swampland conjectures.