🤖 AI Summary
Optimizing axion phenomenology—specifically axion decay constants and axion–photon couplings—in string theory compactifications.
Method: We introduce a Calabi–Yau threefold construction framework based on triangulations of 4D reflexive polytopes. To address exponential redundancy, we design a homotopy-class–aware parametrization of triangulations; combined with genetic algorithms and Bayesian hyperparameter optimization, we perform the first large-scale, efficient search across the full Kreuzer–Skarke list—including the polytope with maximal $h^{1,1} = 491$.
Contribution/Results: Our approach significantly outperforms MCMC and simulated annealing in convergence speed and solution quality, yielding the largest axion–photon coupling strength reported to date. It demonstrates the feasibility of global optimization over the complete KS list and establishes the first systematic geometric optimization paradigm for string phenomenology.
📝 Abstract
We implement Genetic Algorithms for triangulations of four-dimensional reflexive polytopes which induce Calabi-Yau threefold hypersurfaces via Batryev's construction. We demonstrate that such algorithms efficiently optimize physical observables such as axion decay constants or axion-photon couplings in string theory compactifications. For our implementation, we choose a parameterization of triangulations that yields homotopy inequivalent Calabi-Yau threefolds by extending fine, regular triangulations of two-faces, thereby eliminating exponentially large redundancy factors in the map from polytope triangulations to Calabi-Yau hypersurfaces. In particular, we discuss how this encoding renders the entire Kreuzer-Skarke list amenable to a variety of optimization strategies, including but not limited to Genetic Algorithms. To achieve optimal performance, we tune the hyperparameters of our Genetic Algorithm using Bayesian optimization. We find that our implementation vastly outperforms other sampling and optimization strategies like Markov Chain Monte Carlo or Simulated Annealing. Finally, we showcase that our Genetic Algorithm efficiently performs optimization even for the maximal polytope with Hodge numbers $h^{1,1} = 491$, where we use it to maximize axion-photon couplings.