arXiv subjects

Elijah Sheridan

Publications and source records attributed to Elijah Sheridan.

9 recordsLinked to original sources

arXiv2026

Holes in Calabi-Yau Effective Cones

Motivated by their role in non-perturbative potentials in string theory, we study divisors in effective cones of Calabi-Yau threefolds. We give examples of geometries for which some divisor classes in the effective cone are not themselves effective: i.e., they have no global sections. We call these non-holomorphic divisor classes "holes," and characterize their behavior in an ensemble of toric hypersurface Calabi-Yau threefolds. We prove some necessary and sufficient conditions for the existence of holes, show consequences of holes that follow from the minimal model program, and demonstrate that a class of holes come in semigroups (with this class conjectured to constitute all holes). Furthermore, we provide moduli-dependent bounds on the volumes of four-cycles representing holes.

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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.

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arXiv2025

Bayesian inference on Calabi--Yau moduli spaces and the axiverse: experimental data meets string theory

We develop tools of Bayesian inference on the moduli space of Calabi--Yau (CY) manifolds. We sample from the invariant Weil--Petersson (WP) measure using Markov Chain Monte Carlo and normalising flows on \Kahler moduli space with dimension up to $h^{1,1}=30$, and present results on the spectrum of the CY volume and properties of divisors when the measure is restricted in physically meaningful ways. We furthermore present a theory-informed prior on axion masses and decay constants $(m_a,f_a)$ marginalised over the WP measure for all inequivalent CYs constructable from the Kreuzer--Skarke database with $h^{1,1}\leq 5$. We then impose likelihoods based on axion physics. We demonstrate how detection of a relatively heavy QCD axion at small $h^{1,1}$, e.g. by ADMX, provides detailed information about CY geometry and topology. Finally, we compute a full forward model incorporating likelihoods from the cosmic microwave background and Lyman-alpha forest and find the maximum posterior probability region on the moduli space of a given CY favoured by a resolution of the tension in these data by an ultralight axion composing $\mathcal{O}(1\%)$ of the dark matter. This demonstration serves as a blueprint for future statistical analyses within string phenomenology.

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arXiv2024

Fuzzy Axions and Associated Relics

We study fuzzy axion dark matter in type IIB string theory, for axions descending from the Ramond-Ramond four-form in compactifications on orientifolds of Calabi-Yau hypersurfaces. Such models can be tested by cosmological measurements if a significant relic abundance of fuzzy dark matter arises, which we argue is most common in models with small numbers of axions. We construct a topologically exhaustive ensemble of more than 350,000 Calabi-Yau compactifications yielding up to seven axions, and in this setting we perform a systematic analysis of misalignment production of fuzzy dark matter. In typical regions of moduli space, the fuzzy axion, the QCD axion, and other axions have comparable decay constants of $f_a \approx 10^{16}$ GeV. We find that overproduction of heavier axions is problematic, except at special loci in moduli space where decay constant hierarchies can occur: without a contrived reheating epoch, it is necessary to fine-tune initial displacements. The resulting dark matter is typically a mix of fuzzy axions and heavier axions, including the QCD axion. Dark photons are typically present as a consequence of the orientifold projection. We examine the signatures of these models by simulating halos with multiple fuzzy axions, and by computing new cosmological constraints on ultralight axions and dark radiation. We also give evidence that cosmic birefringence is possible in this setting. Our findings determine the phenomenological correlates of fuzzy axion dark matter in a corner of the landscape.

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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.

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arXiv2022

Probing a $\mathrm{Z}^{\prime}$ with non-universal fermion couplings through top quark fusion, decays to bottom quarks, and machine learning techniques

The production of heavy mass resonances has been widely studied theoretically and experimentally. Several extensions of the standard model (SM) of particle physics, naturally give rise to a new resonance, with neutral electric charge, commonly referred to as the $\textrm{Z}^{\prime}$ boson. The nature, mass, couplings, and associated quantum numbers of this hypothetical particle are yet to be determined. We present a feasibility study on the production of a vector like $\textrm{Z}^{\prime}$ boson at the LHC, with preferential couplings to third generation fermions, considering proton-proton collisions at $\sqrt{s} = 13$ $\mathrm{TeV}$ and 14 TeV. We work under two simplified phenomenological frameworks where the $\mathrm{Z}^{\prime}$ masses and couplings to the SM particles are free parameters, and consider final states of the $\textrm{Z}^{\prime}$ decaying to a pair of $\mathrm{b}$ quarks. The analysis is performed using machine learning techniques in order to maximize the experimental sensitivity. The proposed search methodology can be a key mode for discovery, complementary to the existing search strategies considered in literature, and extends the LHC sensitivity to the $\mathrm{Z}^{\prime}$ parameter space.

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arXiv2022

A Survey of Family Unification Models with Bifundamental Matter

Extensions of the Standard Model have been attempted from the bottom up and from the top down yet there remains a largely unexplored middle ground. In this paper, using the Mathematica package LieART, we exhaustively enumerate embeddings of the Standard Model within the class of theories with bifundamental fermions in product gauge group SU(a)XSU(b)XSU(c) with no more generators than E6, while achieving SM family unification rather than replication. We incorporate simple phenomenological constrains and find 151 unique models, including 9 that have only vector-like particle content beyond-the-Standard Model (BSM) particles, which we conjecture belong to 5 infinite families of such models. We describe the potentially most viable models: namely, the 9 with strictly vector-like BSM content along with the 29 models we found with no more than 30 additional BSM chiral particles. These include models with fractional electric charge color singlets, and hence magnetic monopoles with multiple Dirac charge. This latter collection of models predicts chiral particles with masses near the electroweak scale accessible to current and future collider experiments.

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arXiv2021

Magnetars and Axion-like Particles: Probes with the Hard X-ray Spectrum

Quiescent hard X-ray and soft gamma-ray emission from neutron stars constitute a promising frontier to explore axion-like-particles (ALPs). ALP production in the core peaks at energies of a few keV to a few hundreds of keV; subsequently, the ALPs escape and convert to photons in the magnetosphere. The emissivity goes as $\sim T^6$ while the conversion probability is enhanced for large magnetic fields, making magnetars, with their high core temperatures and strong magnetic fields, ideal targets for probing ALPs. We compute the energy spectrum of photons resulting from conversion of ALPs in the magnetosphere and then compare it against hard X-ray data from NuSTAR, INTEGRAL, and XMM-Newton, for a set of eight magnetars for which such data exists. Upper limits are placed on the product of the ALP-nucleon and ALP-photon couplings. For the production in the core, we perform a calculation of the ALP emissivity in degenerate nuclear matter modeled by a relativistic mean field theory. The reduction of the emissivity due to improvements to the one-pion exchange approximation is incorporated, as is the suppression of the emissivity due to proton superfluidity in the neutron star core. A range of core temperatures is considered, corresponding to different models of the steady heat transfer from the core to the stellar surface. For the subsequent conversion, we solve the coupled differential equations mixing ALPs and photons in the magnetosphere. The conversion occurs due to a competition between the dipolar magnetic field and the photon refractive index induced by the external magnetic field. Semi-analytic expressions are provided alongside the full numerical results. We also present an analysis of the uncertainty on the axion limits we derive due to the uncertainties in the magnetar masses, nuclear matter equation of state, and the proton superfluid critical temperature.

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arXiv2021

Probing axion-like particles with $γγ$ final states from vector boson fusion processes at the LHC

We perform a feasibility study to search for axion-like particles (ALPs) using vector boson fusion (VBF) processes at the LHC. We work in an effective field theory framework with cutoff scale $Λ$ and ALP mass $m_{a}$, and assume that ALPs couple to photons with strength $\propto 1/Λ$. Assuming proton-proton collisions at $\sqrt{s} = 13$ TeV, we present the total VBF ALP production cross sections, ALP decay widths and lifetimes, and relevant kinematic distributions as a function of $m_{a}$ and $Λ$. We consider the $a\toγγ$ decay mode to show that the requirement of an energetic diphoton pair combined with two forward jets with large dijet mass and pseudorapidity separation can significantly reduce the Standard Model backgrounds, leading to a $5σ$ discovery reach for $10 \text{ MeV} \lesssim m_{a} \lesssim 1$ TeV with $Λ\lesssim 2$ TeV, assuming an integrated luminosity of 3000 fb$^{-1}$. In particular, this extends the LHC sensitivity to a previously unstudied region of the ALP parameter space.

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