Decoding Nature with Nature's Tools: Heterotic Line Bundle Models of Particle Physics with Genetic Algorithms and Quantum Annealing

TL;DR

This paper demonstrates that genetic algorithms, enhanced with quantum annealing, can efficiently identify viable string compactifications in heterotic string theory, significantly reducing the search space compared to traditional methods.

Contribution

It introduces a novel application of genetic algorithms combined with quantum annealing to explore heterotic string compactifications with improved efficiency and scope.

Findings

Genetic algorithms find nearly all viable solutions in low-dimensional cases.

GA searches on high-dimensional manifolds outperform systematic scans.

Quantum annealing enhances the efficiency of the optimization process.

Abstract

The string theory landscape may include a multitude of ultraviolet embeddings of the Standard Model, but identifying these has proven difficult due to the enormous number of available string compactifications. Genetic Algorithms (GAs) represent a powerful class of discrete optimisation techniques that can efficiently deal with the immensity of the string landscape, especially when enhanced with input from quantum annealers. In this letter we focus on geometric compactifications of the $E_8\times E_8$ heterotic string theory compactified on smooth Calabi-Yau threefolds with Abelian bundles. We make use of analytic formulae for bundle-valued cohomology to impose the entire range of spectrum requirements, something that has not been possible so far. For manifolds with a relatively low number of Kahler parameters we compare the GA search results with results from previous systematic scans, showing that GAs can find nearly all the viable solutions while visiting only a tiny fraction of the solution space. Moreover, we carry out GA searches on manifolds with a larger numbers of Kahler parameters where systematic searches are not feasible.