The Tadpole Problem

TL;DR

The paper conjectures that in F-theory, stabilizing all complex-structure moduli with fluxes at a generic point exceeds the tadpole bound, implying limitations on certain de Sitter vacua constructions.

Contribution

It introduces a conjecture that flux-induced charge growth prevents full moduli stabilization at generic points, supported by examples from K3 x K3 and CP^3 compactifications.

Findings

Flux charge needed exceeds the tadpole bound in large moduli limits.

Supported by examples showing flux charge at 44% of the number of moduli.

Implications for the viability of de Sitter vacua with antibrane uplift.

Abstract

We examine the mechanism of moduli stabilization by fluxes in the limit of a large number of moduli. We conjecture that one cannot stabilize all complex-structure moduli in F-theory at a generic point in moduli space (away from singularities) by fluxes that satisfy the bound imposed by the tadpole cancelation condition. More precisely, while the tadpole bound in the limit of a large number of complex-structure moduli goes like 1/4 of the number of moduli, we conjecture that the amount of charge induced by fluxes stabilizing all moduli grows faster than this, and is therefore larger than the allowed amount. Our conjecture is supported by two examples: K3 x K3 compactifications, where by using evolutionary algorithms we find that moduli stabilization needs fluxes whose induced charge is 44% of the number of moduli, and Type IIB compactifications on CP^3, where the induced charge of the fluxes needed to stabilize the D7-brane moduli is also 44% of the number of these moduli. Proving our conjecture would rule out de Sitter vacua obtained via antibrane uplift in long warped throats with a hierarchically small supersymmetry breaking scale, which require a large tadpole.