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A<sc>bstract</sc> We study moduli stabilization via fluxes in the 2⁶Landau-Ginzburg model. Fluxes not only give masses to scalar fields but can also induce higher order couplings that stabilize massless fields. We investigate this for several different flux choices in the 2⁶model and find two examples that are inconsistent with the Refined Tadpole Conjecture. We also present, to our knowledge, the first 4d$$ \mathcal{N} $$ $N$= 1 Minkowski solution in string theory without any flat direction. 

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<sc>bstract</sc> Calabi-Yau compactifications have typically a large number of complex structure and/or Kähler moduli that have to be stabilised in phenomenologically-relevant vacua. The former can in principle be done by fluxes in type IIB solutions. However, the tadpole conjecture proposes that the number of stabilised moduli can at most grow linearly with the tadpole charge of the fluxes required for stabilisation. We scrutinise this conjecture in the 2⁶Gepner model: a non-geometric background mirror dual to a rigid Calabi-Yau manifold, in the deep interior of moduli space. By constructing an extensive set of supersymmetric Minkowski flux solutions, we spectacularly confirm the linear growth, while achieving a slightly higher ratio of stabilised moduli to flux charge than the conjectured upper bound. As a byproduct, we obtain for the first time a set of solutions within the tadpole bound where all complex structure moduli are massive. Since the 2⁶model has no Kähler moduli, these show that the massless Minkowski conjecture does not hold beyond supergravity. 

A<sc>bstract</sc> In this paper we present a large class of flux backgrounds and solve the shortest vector problem in type IIB string theory on an orientifold of the 1⁹Landau-Ginzburg model. 

A<sc>bstract</sc> We describe the linearized supergeometry of eleven dimensional supergravity with four off-shell local supersymmetries. We start with a background Minkowski 11D, N=1 superspace, and an additional ingredient of a global, constant,G₂-structure which facilitates the definition of a 4|4 + 7 background superspace. A bottom-up construction of linear fluctuations of the geometric constituents (such as supervielbein, spin connection, and the super 3-form of 11D supergravity) is given in terms of 4D, N=1 prepotential superfields. This is complemented by a top-down description of the linearized supergeometry of the 4|4 + 7 superspace dealing directly with torsion, curvature, and Bianchi identities. Torsion constraints that (combined with the Bianchi identities) lead to the preceding prepotential expressions of the gauge fields are identified. All irreducible consequences of the torsion and 4-form Bianchi identities are systematically derived except for dimension 2 Bianchi identities of the 4-form, and dimension$$ \frac{5}{2} $$ $\frac{5}{2}$Bianchi identities of torsion, which set bosonic curls of components of one lower dimension to zero. 

A bstract We derive the component structure of 11D, N = 1/8 supergravity linearized around eleven-dimensional Minkowski space. This theory represents 4 local supersymmetries closing onto 4 of the 11 spacetime translations without the use of equations of motion. It may be interpreted as adding 201 auxiliary bosons and 56 auxiliary fermions to the physical supergravity multiplet for a total of 376 + 376 components. These components and their transformations are organized into representations of SL(2; C ) × G 2 .