Algorithmically solving the Tadpole Problem

Understand

The extensive computer-aided search applied in [arXiv:2010.10519] to find the minimal charge sourced by the fluxes that stabilize all the (flux-stabilizable) moduli of a smooth K3xK3 compactification uses differential evolutionary algorithms supplemented by local searches.

• We present these algorithms in detail and show that they can also solve our minimization problem for other lattices.
• Our results support the Tadpole Conjecture: The minimal charge grows linearly with the dimension of the lattice and, for K3xK3, this charge is larger than allowed by tadpole cancelation.
• Even if we are faced with an NP-hard lattice-reduction problem at every step in the minimization process, we find that differential evolution is a good technique for identifying the regions of the landscape where the fluxes with the lowest tadpole can be found.