Tadpole conjecture in non-geometric backgrounds

TL;DR

This paper investigates the tadpole conjecture in a non-geometric string theory background, confirming the linear growth of stabilized moduli with flux charge and providing new solutions with all complex structure moduli massive.

Contribution

It provides the first extensive set of supersymmetric Minkowski flux solutions in a non-geometric background, confirming the linear growth of stabilized moduli and challenging the massless Minkowski conjecture.

Findings

Confirmed linear growth of stabilized moduli with flux charge

Achieved higher ratio of stabilized moduli than the conjectured bound

Found solutions with all complex structure moduli massive within the tadpole bound

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 $2^6$ 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 $2^6$ model has no K\"ahler moduli, these show that the massless Minkowski conjecture does not hold beyond supergravity.