Tadpole conjecture in non-geometric backgrounds
Abstract
Calabi-Yau compactifications have typically a large number of complex structure and/or K\"ahler 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 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 model has no K\"ahler moduli, these show that the massless Minkowski conjecture does not hold beyond supergravity.
Cite
@article{arxiv.2407.16758,
title = {Tadpole conjecture in non-geometric backgrounds},
author = {Katrin Becker and Nathan Brady and Mariana Graña and Miguel Morros and Anindya Sengupta and Qi You},
journal= {arXiv preprint arXiv:2407.16758},
year = {2025}
}
Comments
33 pages, 2 figures. Bibliography contains a GitHub link to the accompanying codes and dataset. v2: We corrected a crucial factor of 2 in comparing to the tadpole conjecture (Ref. [13]), which uses a different convention for the flux charge