arXiv subjects

Andreas Schachner

Publications and source records attributed to Andreas Schachner.

At least 19 recordsLinked to original sources

arXiv2026

Parameter compression in the flux landscape

We present a data-driven investigation of the exhaustive ensemble of no-scale type IIB flux vacua constructed in \cite{Chauhan:2025rdj}. Using a combination of linear and non-linear dimensionality-reduction techniques, we analyse both flux and moduli spaces and demonstrate that the effective dimensionality of the underlying 12-dimensional flux space is substantially reduced. A central component of our study is a physics-informed autoencoder, which provides a non-linear compression of the flux and moduli data into a low-dimensional latent space. The learned latent representation organises vacua according to desired features and, in particular, isolates distinguished regions associated with small values of the flux superpotential $|W_0|$, revealing non-trivial correlations that are not captured by linear methods. In parallel, we apply tools from topological data analysis, specifically persistent homology, to probe the global structure of the vacuum distribution. This allows us to identify robust, long-lived topological features in both moduli and flux subspaces. This work is a necessary step for developing foundation models in string phenomenology.

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arXiv2025

Effective potentials, warping, and implications for F-term uplifting

We analyse warping corrections to the scalar potential in flux compactifications of Type IIB string theory, focusing on their effect on $F$-term de Sitter uplifting in Calabi-Yau orientifold models. A systematic inverse-volume expansion allows us to derive the four-dimensional off-shell potential in the presence of warping and non-ISD 3-form fluxes. This corresponds to integrating out all massive Kaluza-Klein modes using the ten-dimensional equations of motion. We further propose a warped K\"ahler potential in four-dimensional $\mathcal{N}=1$ supergravity, and show that it is consistent with our ten-dimensional results. In the KKLT framework, we find that classical warping corrections, as well as mixed corrections involving non-ISD fluxes and quantum effects, are dominant, rendering the scenario effectively uncontrollable with current methods. By contrast, in LVS-like constructions these corrections are suppressed by inverse powers of the volume, specifically $\mathcal{V}^{1/2}$ or $\mathcal{V}^{1/6}$, depending on the concrete model.

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arXiv2025

TASI Lectures on de Sitter Vacua

These lectures provide a self-contained introduction to flux compactifications of type IIB string theory on Calabi-Yau orientifolds. The first lecture begins with geometric foundations, then presents vacuum solutions in Calabi-Yau compactifications, as well as the geometry and physics of the moduli problem. The second lecture develops the classical theory of type IIB flux compactifications, both in ten dimensions and in the four-dimensional effective theory. The third lecture turns to the quantum theory of flux compactifications, including perturbative and non-perturbative corrections. With this foundation, in the fourth lecture we give a detailed treatment of the candidate de Sitter vacua recently constructed in arXiv:2406.13751. These notes are intended to be accessible to graduate students working in adjacent fields, and so extensive background material is included throughout.

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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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arXiv2025

Type IIB at eight derivatives: Five-Point Axio-Dilaton Couplings

We study the Type IIB eight-derivative effective Lagrangian beyond the quartic level, focusing on interactions involving gravitons and axio-dilatons. We show how to translate five-point scattering amplitudes into genuine five-point contact terms and extract all perturbative contributions to the effective action. Our result is consistent with T-duality predictions at tree level in the NSNS sector. We find that couplings with an even/odd number of scalars are neutral/charged under $\mathrm{SL}(2,\mathbb{Z})$, and use this feature to deduce their non-perturbative completion. The mixed NSNS/RR structures that cannot be deduced from the pure NSNS sector allow us to unambiguously fix the kinematics, which turns out to be the same for tree level and one loop. In Type IIA, these structures are essential for establishing agreement of string-theoretic corrections with the circle reduction of M-theory higher-derivative couplings.

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arXiv2025

Coexisting Flux String Vacua from Numerical K\"ahler Moduli Stabilisation

We present a comprehensive study of K\"ahler moduli stabilisation in Type IIB flux compactifications, combining advanced numerical techniques with analytical methods. Our JAX-based computational framework enables efficient scanning of the UV parameter space, while incorporating $\alpha'$ corrections, loop and non-perturbative effects, as well as uplift contributions to the scalar potential. The implementation features rigorous vacuum validation protocols derived from analytic results. We apply our methods to explicit flux compactifications on more than 80,000 Calabi-Yau threefolds with $h^{1,1}\leq 6$ K\"ahler moduli. By systematically scanning over a wide range of values of the flux superpotential $W_0$ and the string coupling $g_s$, we find explicit realisations of every established K\"ahler moduli stabilisation scenario: for $10^{-15} \leq |W_0| \leq 10^{-2}$ we obtain both KKLT-like and K\"ahler uplifted vacua, while for the broader range $10^{-1} \leq |W_0| \leq 10^2$ we recover LVS as well as LVS-like hybrid solutions. Notably, we discover significant parameter regions where multiple vacua coexist within a single flux potential, including novel configurations pairing AdS, Minkowski, and dS minima with different volume hierarchies. These findings enable, for the first time, the analysis of vacuum decay processes within fixed flux configurations, complementing the established theory of transitions between distinct flux vacua and decays towards decompactification.

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arXiv2025

Brief overview of Candidate de Sitter Vacua

We review compactifications of type IIB string theory which produce de Sitter vacua to leading order in the $\alpha^\prime$ and $g_s$ expansions in line with the scenario proposed by Kachru, Kallosh, Linde, and Trivedi. We detail specific Calabi-Yau orientifold compactifications incorporating the non-perturbative superpotential from Euclidean D3-branes, the full flux-induced superpotential, and the K\"ahler potential evaluated at string tree level but retaining all orders in $\alpha'$. Each model hosts a Klebanov-Strassler throat featuring a single anti-D3-brane. The energy associated with this supersymmetry-breaking source, computed at leading order in $\alpha'$, lifts the minimum to a metastable de Sitter vacuum with all moduli stabilised. A key open challenge is the identification of vacua that remain stable when including additional corrections; an endeavour for which this study provides a solid foundation. This work is a contribution to the proceedings of the Corfu Summer Institute 2024 "School and Workshops on Elementary Particle Physics and Gravity" (CORFU2024) and is based on arXiv:2406.13751.

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arXiv2025

A Fuzzy Axiverse from String Theory

In this talk, I showcase models for fuzzy axion dark matter within the framework of type IIB string theory, focusing on axions originating from the Ramond-Ramond four-form in compactifications on Calabi-Yau orientifold hypersurfaces. These models are amenable to cosmological tests if a substantial relic abundance of fuzzy dark matter is produced. I present a topologically exhaustive ensemble of more than 350{,}000 Calabi-Yau compactifications with up to seven axions together with a systematic analysis of the misalignment production of fuzzy dark matter. The resulting dark matter composition is generally a mixture of fuzzy axions and heavier axions, including the QCD axion. Dark photons frequently emerge due to the orientifold projection. I will also comment on applications of optimisation strategies based on automatic differentiation for exploring the string axiverse. This talk is partially based on arXiv:2412.12012.

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arXiv2025

Deep observations of the Type IIB flux landscape

We present deep observations in targeted regions of the string landscape through a combination of analytic and dedicated numerical methods. Specifically, we devise an algorithm designed for the systematic construction of Type IIB flux vacua in finite regions of moduli space. Our algorithm is universally applicable across Calabi-Yau orientifold compactifications and can be used to enumerate flux vacua in a region given sufficient computational efforts. As a concrete example, we apply our methods to a two-modulus Calabi-Yau threefold, demonstrating that systematic enumeration is feasible and revealing intricate structures in vacuum distributions. Our results highlight local deviations from statistical expectations, providing insights into vacuum densities, superpotential distributions, and moduli mass hierarchies. This approach opens pathways for precise, data-driven mappings of the string landscape, complementing analytic studies and advancing the understanding of the distribution of flux vacua. This allows us to obtain different types of solutions with hierarchical suppressions, e.g.~vacua with small values of the Gukov-Vafa-Witten superpotential $|W_0|$. We find an example with $|W_0| = 5.547 \times 10^{-5}$ at large complex structure, without light directions and the use of non-perturbative effects.

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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

Cambridge Lectures on The Standard Model

These lecture notes cover the Standard Model (SM) course for Part III of the Cambridge Mathematical Tripos, taught during the years 2020-2023. The course comprised 25 lectures and 4 example classes. Following a brief historical introduction, the SM is constructed from first principles. We begin by demonstrating that essentially only particles with spin/helicity $0, \frac{1}{2}, 1, \frac{3}{2}, 2$ can describe matter and interactions, using spacetime symmetries, soft theorems, gauge redundancies, Ward identities, and perturbative unitarity. The remaining freedom lies in the choice of the Yang-Mills gauge group and matter representations. Effective field theories (EFTs) are a central theme throughout the course, with the 4-Fermi interactions and chiral perturbation theory serving as key examples. Both gravity and the SM itself are treated as EFTs, specifically as the SMEFT (Standard Model Effective Field Theory). Key phenomenological aspects of the SM are covered, including the Higgs mechanism, Yukawa couplings, the CKM matrix, the GIM mechanism, neutrino oscillations, running couplings, and asymptotic freedom. The discussion of anomalies and their non-trivial cancellations in the SM is detailed. Simple examples of calculations, such as scattering amplitudes and decay rates, are provided. The course concludes with a brief overview of the limitations of the SM and an introduction to the leading proposals for physics beyond the Standard Model.

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arXiv2024

Candidate de Sitter Vacua

We construct compactifications of type IIB string theory that yield, at leading order in the $\alpha^\prime$ and $g_s$ expansions, de Sitter vacua of the form envisioned by Kachru, Kallosh, Linde, and Trivedi. We specify explicit Calabi-Yau orientifolds and quantized fluxes for which we derive the four-dimensional effective supergravity theories, incorporating the exact flux superpotential, the nonperturbative superpotential from Euclidean D3-branes, and the K\"ahler potential at tree level in the string loop expansion but to all orders in $\alpha'$. Each example includes a Klebanov-Strassler throat region containing a single anti-D3-brane, whose supersymmetry-breaking energy, computed at leading order in $\alpha'$, causes an uplift to a metastable de Sitter vacuum in which all moduli are stabilized. Finding vacua that demonstrably survive subleading corrections, and in which the quantization conditions are completely understood, is an important open problem for which this work has prepared the foundations.

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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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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 $h^{1,1} =2$.

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arXiv2023

Testing BSM Physics with Gravitational Waves

The Cosmic Gravitational Wave Background (CGWB) is an irreducible background of gravitational waves generated by particle exchange in the early Universe plasma. Standard Model particles contribute to such a stochastic background with a peak at $f\sim 80$ GHz. Any physics beyond the Standard Model (BSM) may modify the CGWB spectrum, making it a potential testing ground for BSM physics. We consider the impact of general BSM scenarios on the CGWB, including an arbitrary number of hidden sectors. We find that the largest amplitude of the CGWB comes from the sector that dominates the energy density after reheating and confirm the dominance of the SM for standard cosmological histories. For non-standard cosmological histories, such as those with a stiff equation of state $ω>1/3$, like in kination, BSM physics may dominate and modify the spectrum substantially. We conclude that, if the CGWB is detected at lower frequencies and amplitudes compared to that of the SM, it will hint at extra massive degrees of freedom or hidden sectors. If it is instead measured at higher values, it will imply a period with $ω>1/3$. We argue that for scenarios with periods of kination in the early Universe, a significant fraction of the parameter space can be ruled out from dark radiation bounds at BBN.

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arXiv2023

New non-supersymmetric flux vacua in string theory

In this note we construct large ensembles of supersymmetry breaking solutions arising in the context of flux compactifications of type IIB string theory. This class of solutions was previously proposed in arXiv:hep-th/0402135 for which we provide the first explicit examples in Calabi-Yau orientifold compactifications with discrete fluxes below their respective tadpole constraint. As a proof of concept, we study the degree 18 hypersurface in weighted projective space $\mathbb{CP}_{1,1,1,6,9}$. Furthermore, we look at 10 additional orientifolds with $h^{1,2}=2,3$. We find several flux vacua with hierarchical suppression of the vacuum energy with respect to the gravitino mass. These solutions provide a crucial stepping stone for the construction of explicit de Sitter vacua in string theory. Lastly, we also report the difference in the distribution of $W_0$ between supersymmetric and non-supersymmetric minima.

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arXiv2023

W0_sample = np.random.normal(0,1)?

In this note we explore the distribution of vacuum expectation values of the superpotential $W_0$ in explicit Type IIB flux compactifications. We show that the distribution can be approximated, universally across geometries, by a two-dimensional Gaussian with a model dependent standard deviation. We identify this behaviour in 20 Calabi-Yau orientifold compactifications with between two and five complex structure moduli by constructing a total of $\mathcal{O}(10^7)$ flux vacua. We observe a characteristic scaling behaviour of the width $σ$ of our distributions with respect to the D3-charge contributions $N_{\text{flux}}$ from fluxes which can be approximated by $σ\sim \sqrt{N_{\text{flux}}}$. This $W_0$ distribution implies that locating small values of $|W_0|$ as a preferred regime associated with classes of string theory solutions typically featuring hierarchies, simplifies to the basic statement of finding small Euclidean norms of normally distributed values. We do also identify small modifications to this Gaussian behaviour in our samples which might be seen as indications for the breakdown of the continuous flux approximation commonly used in the context of statistical analyses of the flux landscape.

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arXiv2023

JAXVacua -- A Framework for Sampling String Vacua

Moduli stabilisation in string compactifications with many light scalars remains a major blind-spot in the string landscape. In these regimes, analytic methods cease to work for generic choices of UV parameters which is why numerical techniques have to be exploited. In this paper, we implement algorithms based on JAX, heavily utilising automatic differentiation, just-in-time compilation and parallelisation features, to efficiently construct string vacua. This implementation provides a golden opportunity to efficiently analyse large unexplored regions of the string landscape. As a first example, we apply our techniques to the search of Type IIB flux vacua in Calabi-Yau orientifold compactifications. We argue that our methods only scale mildly with the Hodge numbers making exhaustive studies of low energy effective field theories with $\mathcal{O}(100)$ scalar fields feasible. Using small computing resources, we are able to construct $\mathcal{O}(10^6)$ flux vacua per geometry with $h^{1,2}\geq 2$, vastly out-performing previous systematic searches. In particular, we showcase the efficiency of our methods by presenting generic vacua with fluxes below the tadpole constraint set by the orientifold with up to $h^{1,2}=25$ complex structure moduli.

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