Algorithmically solving the Tadpole Problem

TL;DR

This paper develops and applies differential evolutionary algorithms and a novel 'Spider Algorithm' to efficiently find minimal flux charges in string compactifications, supporting the Tadpole Conjecture that minimal charges grow with lattice dimension.

Contribution

It introduces detailed algorithms, including the new 'Spider Algorithm', for solving flux minimization problems in string theory compactifications, demonstrating their effectiveness across different lattices.

Findings

Minimal charge grows linearly with lattice dimension.

Differential evolution effectively identifies low-tadpole regions.

The 'Spider Algorithm' efficiently finds many minimal-tadpole configurations.

Abstract

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. We then design a "Spider Algorithm," which is very efficient at exploring these regions and producing large numbers of minimal-tadpole configurations.