The Tadpole Problem

Understand

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.