arXiv subjects

Nate MacFadden

Publications and source records attributed to Nate MacFadden.

7 recordsLinked to original sources

arXiv2026

Sampling Triangulations and Calabi-Yau Threefolds with Autoregressive GNNs

We introduce `dualGNN', an autoregressive message-passing GNN for sampling fine, regular triangulations of lattice polytopes. dualGNN operates on a generalization of the dual graph of a triangulation, with edges labeled by `signed circuits' -- combinatorial invariants from the theory of oriented matroids. We show that these circuits are necessary and sufficient to determine a triangulation's regularity from the graph, provided certain magnitude information is retained. The model is independent of the polytope's point count and invariant under its orientation-preserving symmetries ($\mathrm{SL}(d,\mathbb{Z}) \ltimes \mathbb{Z}^d$), and our masking procedure further guarantees that every rollout produces a fine triangulation (in 2D). On unseen polygons with $N_\mathrm{pts} \leq 40$, dualGNN is the only sampler we tested that is consistent with uniform sampling across all our diagnostics (KL divergence from uniformity, collision counts, and sample autocorrelation). The model is small ($\sim92$k parameters) and trains in $\sim7.5$ hours on a single consumer GPU. We apply dualGNN to string theory, sampling Calabi-Yau threefolds uniformly at $h^{1,1}=86$; we also sample CYs at $h^{1,1}=128$, observing no deviations from uniformity, but our diagnostics are weaker here. Code, training scripts, and pretrained models are available at https://github.com/natemacfadden/dualGNN (pip install dualgnn), and dualGNN is integrated into CYTools.

hep-th↗

arXiv2026

Further Bounding the Kreuzer-Skarke Landscape

Batyrev's construction provides a map from fine, regular, star triangulations (FRSTs) of 4D reflexive polytopes to smooth Calabi-Yau threefolds (CYs). We prove that there are at most $10^{296}$ diffeomorphism classes of CYs produced in this manner, improving arXiv:2008.01730's upper bound of $10^{428}$. To show this, we make use of the fact that any two FRSTs with the same 2-face restrictions give rise to diffeomorphic CYs and bound the number of such '2-face equivalence classes' for all polytopes with Hodge number $h^{1,1} \geq 300$. We also put a lower bound of $10^{276}$ on the number of 2-face equivalence classes, but emphasize that this is not a lower bound on the number of diffeomorphism classes of CYs, as distinct 2-face equivalence classes may give rise to diffeomorphic threefolds.

hep-th↗

arXiv2025

Calabi-Yau Threefolds from Vex Triangulations

We study the birational geometry (i.e., K\"ahler moduli space) of Calabi--Yau (CY) threefold hypersurfaces in toric varieties arising from four-dimensional reflexive polytopes. In particular, it has been observed that the birational classes of these geometries are not exhausted by toric hypersurfaces arising from fine, regular, star triangulations (FRSTs). We begin by introducing a classification problem: enumeration of birational classes of toric varieties, which is equivalent to enumeration of certain triangulations/fans. We consider this problem from the complementary perspectives of triangulation theory and toric geometry, reviewing both theories in detail; this culminates in an explanation of how to generate all fine regular triangulations of a vector configuration (i.e., fine regular simplicial fans) which we implement in a Python package regfans [1]. We then apply this theory to the Kreuzer--Skarke (KS) database, where we encounter both FRSTs and vex triangulations. We study the non-weak-Fano toric varieties arising from vex triangulations, along with their CY hypersurfaces. In particular, we show that all fine regular triangulations of a fixed 4D reflexive polytope give rise to smooth birational CY hypersurfaces, extending Batyrev's result from FRSTs to vex triangulations. We exhaustively enumerate all $24,023,940$ fine regular triangulations in the KS database with $h^{1,1}\leq 7$, of which over $70\%$ are vex triangulations, and provide an upper bound of $10^{979}$ for fine regular triangulations in the entire KS database. We conclude that vex triangulations of four-dimensional reflexive polytopes give rise to a large number of smooth Calabi--Yau threefolds and importantly provide toric descriptions for novel regions in the K\"ahler moduli space.

hep-th↗

arXiv2024

The DNA of Calabi-Yau Hypersurfaces

We implement Genetic Algorithms for triangulations of four-dimensional reflexive polytopes which induce Calabi-Yau threefold hypersurfaces via Batyrev'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. Our methods for sampling and optimization are implemented in a Python package cyopt.

hep-th↗

arXiv2023

Counting Calabi-Yau Threefolds

We enumerate topologically-inequivalent compact Calabi-Yau threefold hypersurfaces. By computing arithmetic and algebraic invariants and the Gopakumar-Vafa invariants of curves, we prove that the number of distinct simply connected Calabi-Yau threefold hypersurfaces resulting from triangulations of four-dimensional reflexive polytopes is 4, 27, 183, 1,184 and 8,036 at $h^{1,1}$ = 1, 2, 3, 4, and 5, respectively. We also establish that there are ten equivalence classes of Wall data of non-simply connected Calabi-Yau threefolds from the Kreuzer-Skarke list. Finally, we give a provisional count of threefolds obtained by enumerating non-toric flops at $h^{1,1} =2$.

hep-th↗

arXiv2023

Efficient Algorithm for Generating Homotopy Inequivalent Calabi-Yaus

We present an algorithm for efficiently exploring inequivalent Calabi-Yau threefold hypersurfaces in toric varieties. A direct enumeration of fine, regular, star triangulations (FRSTs) of polytopes in the Kreuzer-Skarke database is foreseeably impossible due to the large count of distinct FRSTs. Moreover, such an enumeration is needlessly redundant because many such triangulations have the same restrictions to 2-faces and hence, by Wall's theorem, lead to equivalent Calabi-Yau threefolds. We show that this redundancy can be circumvented by finding a height vector in the strict interior of the intersection of the secondary cones associated with each 2-face triangulation. We demonstrate that such triangulations are generated with orders of magnitude fewer operations than the naive approach of generating all FRSTs and selecting only those differing on 2-faces. Similar methods are also presented to directly generate (the support of) the secondary subfan of all fine triangulations, relevant for random sampling of FRSTs.

hep-th↗

arXiv2021

Search for Dark Photon Dark Matter: Dark E-Field Radio Pilot Experiment

We are building an experiment to search for dark matter in the form of dark photons in the nano- to milli-eV mass range. This experiment is the electromagnetic dual of magnetic detector dark radio experiments. It is also a frequency-time dual experiment in two ways: We search for a high-Q signal in wide-band data rather than tuning a high-$Q$ resonator, and we measure electric rather than magnetic fields. In this paper we describe a pilot experiment using room temperature electronics which demonstrates feasibility and sets useful limits to the kinetic coupling $ε\sim 10^{-12}$ over 50--300 MHz. With a factor of 2000 increase in real-time spectral coverage, and lower system noise temperature, it will soon be possible to search a wide range of masses at 100 times this sensitivity. We describe the planned experiment in two phases: Phase-I will implement a wide band, 5-million channel, real-time FFT processor over the 30--300 MHz range with a back-end time-domain optimal filter to search for the predicted $Q\sim 10^6$ line using low-noise amplifiers. We have completed spot frequency calibrations using a biconical dipole antenna in a shielded room that extrapolate to a $5 σ$ limit of $ε\sim 10^{-13}$ for the coupling from the dark field, per month of integration. Phase-II will extend the search to 20 GHz using cryogenic preamplifiers and new antennas.

physics.ins-det↗