Finiteness theorems and counting conjectures for the flux landscape

We perform a detailed study of (supersymmetric) moduli stabilisation in type IIB toroidal orientifolds with fluxes. We provide strong evidence towards exhaustion of the finite number of inequivalent vacua for a given total 3-form flux charge N flux. We also find that the minimal value of the string coupling g s is given in terms of N flux and present strong evidence for the asymptotic relation g s, min ∼ $$ c/{N}_{\textrm{flux}}^{\alpha } $$ c / N flux α , with α = 1, 2, valid for not too small N flux, where c is an order 1 coefficient and α depends on the orbifold. Imposing tadpole cancellation, N flux is bounded from the number of orientifold O3-planes. Combined with the flux quantisation, this forbids orientifold vacua without anti-brane charge. On the other hand, the presence of negative D3-brane charge induced by magnetised D7-branes breaks supersymmetry and relaxes the bound, allowing significantly smaller values for g s .

Flux vacua in type IIB compactifications on orbifolds: their finiteness and minimal string coupling

Antoniadis,

Guillen,

Lacombe

2024

End of the world brane networks for infinite distance limits in CY moduli space

Angius

2024

Dynamical Cobordism provides a powerful method to probe infinite distance limits in moduli/field spaces parameterized by scalars constrained by generic potentials, employing configurations of codimension-1 end of the world (ETW) branes. These branes, characterized in terms of critical exponents, mark codimension-1 boundaries in the spacetime in correspondence of finite spacetime distance singularities at which the scalars diverge. Using these tools, we explore the network of infinite distance singularities in the complex structure moduli space of Calabi-Yau fourfolds compactifications in M-theory with a four-form flux turned on, which is described in terms of normal intersecting divisors classified by asymptotic Hodge theory. We provide spacetime realizations for these loci in terms of networks of intersecting codimension-1 ETW branes classified by specific critical exponents which encapsulate the relevant information of the asymptotic Hodge structure characterizing the corresponding divisors.

Tadpole conjecture in non-geometric backgrounds

Becker,

Brady,

Graña

et al. 2024

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 26 Gepner 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 26 model has no Kähler moduli, these show that the massless Minkowski conjecture does not hold beyond supergravity.