Analytics of type IIB flux vacua and their mass spectra

We investigate a relationship between a particular class of two-dimensional integrable non-linear σ-models and variations of Hodge structures. Concretely, our aim is to study the classical dynamics of the λ-deformed G/G model and show that a special class of solutions to its equations of motion precisely describes a one-parameter variation of Hodge structures. We find that this special class is obtained by identifying the group-valued field of the σ-model with the Weil operator of the Hodge structure. In this way, the study of strings on classifying spaces of Hodge structures suggests an interesting connection between the broad field of integrable models and the mathematical study of period mappings.

Section: A Generalized Tadpole Conjecture For the Hodge Locusmentioning

confidence: 99%

“…In other words, it is related to the existence of a flat direction in the scalar potential. For related work on the tadpole conjecture, we refer the reader to [42][43][44][45][46][47][48][49][50].…”

Section: Introductionmentioning

confidence: 99%

Deformed WZW models and Hodge theory. Part I

Grimm

Jeroen

2022

Symmetric fluxes and small tadpoles

Coudarchet,

Marchesano,

Prieto

et al. 2023

The analysis of type IIB flux vacua on warped Calabi-Yau orientifolds becomes considerably involved for a large number of complex structure fields. We however show that, for a quadratic flux superpotential, one can devise simplifying schemes which effectively reduce the large number of equations down to a few. This can be achieved by imposing the vanishing of certain flux quanta in the large complex structure regime, and then choosing the remaining quanta to respect the symmetries of the underlying prepotential. One can then implement an algorithm to find large families of flux vacua with a fixed flux tadpole, independently of the number of fields. We illustrate this approach in a Calabi-Yau manifold with 51 complex structure moduli, where several reduction schemes can be implemented in order to explicitly solve the vacuum equations for that sector. Our findings display a flux-tadpole-to-stabilized-moduli ratio that is marginally above the bound proposed by the Tadpole Conjecture, and we discuss several effects that would take us below such a bound.

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.