Moduli-dependent Calabi-Yau and SU(3)-structure metrics from Machine Learning

Anderson, Lara B.; Gerdes, Mathis; Gray, J. I.; Krippendorf, Sven; Raghuram, Nikhil; Ruehle, Fabian

doi:10.48550/arxiv.2012.04656

Cited by 5 publications

(6 citation statements)

References 31 publications

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“…This work also nicely relates to the current efforts to apply the techniques from machine learning and AI in the study of string vacua [54][55][56]. For example, machine learned Calabi-Yau metrics [57][58][59][60][61] can be used to find Yukawa couplings in string compactifications to the SM. Furthermore, we would also like to understand the role of modular invariance for modeling of the observed masses and couplings [62].…”

Section: Inflation and Its Possible Relation To Dark Energymentioning

confidence: 70%

Quantum Gravity and Phenomenology: Dark Matter, Dark Energy, Vacuum Selection, Emergent Spacetime, and Wormholes

Berglund¹,

Dai²,

Edmonds³

et al. 2022

Preprint

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We discuss the relevance of quantum gravity to the frontier questions in high energy phenomenology: the problems of dark matter, dark energy, and vacuum selection as well as the problems of emergent spacetime and wormholes. Dark matter and dark energy phenomenology, and the problem of vacuum selection are discussed within the context of string theory as a model of quantum gravity. Emergent spacetime and wormholes are discussed in a more general context of effective theories of quantum gravity.

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Section: Inflation and Its Possible Relation To Dark Energymentioning

confidence: 70%

Quantum Gravity and Phenomenology: Dark Matter, Dark Energy, Vacuum Selection, Emergent Spacetime, and Wormholes

Berglund¹,

Dai²,

Edmonds³

et al. 2022

Preprint

View full text Add to dashboard Cite

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“…There are no known analytic expressions for metrics on non-trivial Calabi-Yau threefolds. Fortunately, there are now many ways to obtain such metrics numerically, including position-space methods [26] and a number of spectral methods such as balanced metrics [9,10,27,28], optimal metrics [11], and, more recently, machine learning and neural networks [13][14][15].…”

Section: A Numerical Cy Metricsmentioning

confidence: 99%

“…Almost simultaneously with the rekindled interest in the swampland program, machine learning techniques were introduced to string theory [3][4][5][6] (see [7] for a review). While numerical algorithms for computing CY metrics have been studied before [8][9][10][11], the advent of faster optimizers and computers have made the analysis amendable to machine learning CY metrics [12][13][14][15], even at many different points in complex structure moduli space. Once the (moduli-dependent) Calabi-Yau metric is known, the spectrum of massive string excitations can be computed numerically [16,17].…”

Section: Introductionmentioning

confidence: 99%

Moduli-dependent KK towers and the swampland distance conjecture on the quintic Calabi-Yau manifold

Ashmore,

Ruehle

2021

Preprint

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We use numerical methods to obtain moduli-dependent Calabi-Yau metrics and from them the moduli-dependent massive tower of Kaluza-Klein states for the one-parameter family of quintic Calabi-Yau manifolds. We then compute geodesic distances in their Kähler and complex structure moduli space using exact expressions from mirror symmetry, approximate expressions, and numerical methods and compare the results. Finally, we fit the moduli-dependence of the massive spectrum to the geodesic distance to obtain the rate at which states become exponentially light. The result is indeed of order one, as suggested by the swampland distance conjecture. We also observe levelcrossing in the eigenvalue spectrum and find that states in small irreducible representations of the symmetry group tend to become lighter than states in larger irreducible representations. CONTENTS I. Introduction 1 II. Geodesics in moduli space 2 A. Geodesics in complex structure moduli space 2 B. Geodesics in Kähler moduli space 3 C. Geodesics for the one-parameter quintic 3 Complex structure moduli space 3 Kähler moduli space 4 III. CY metric and massive spectrum 5 A. Numerical CY metrics 5 B. The spectrum of the Laplace operator 5 C. Numerical results 6 IV. Conclusions and Outlook 7 Acknowledgments 8 A. Einstein frame masses 8 B. Symmetries of the family of quintics 8 References 9

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“…Our work establishes the foundation of future endeavors in this direction, which consists in describing what leptoquarks can be realized in string constructions. In this work, we provide some tools to address these questions by either inspecting systematically the properties of the identified models or applying machine learning techniques, as has been done recently in the SUSY case [15,16,[60][61][62][63][64][65][66][67][68][69][70][71][72][73].…”

Section: Introductionmentioning

confidence: 99%

The landscape of promising non-supersymmetric string models

Perez-Martinez,

Ramos-Sanchez,

Vaudrevange

2021

Preprint

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Leptoquarks extending the Standard Model (SM) are attracting an increasing attention in the recent literature. Hence, the identification of 4D SM-like models and the classification of allowed leptoquarks from strings is an important step in the study of string phenomenology. We perform the most extensive search for SM-like models from the nonsupersymmetric heterotic string SO(16) × SO(16), resulting in more than 170,000 inequivalent promising string models from 138 Abelian toroidal orbifolds. We explore the 4D massless particle spectra of these models in order to identify all exotics beside the three generations of quarks and leptons. Hereby, we learn which leptoquark can be realized in this string setup. Moreover, we analyze the number of SM Higgs doublets which is generically larger than one. Then, we identify SM-like models with a minimal particle content. These so-called almost SM models appear most frequently in the orbifold geometries Z 2 ×Z 4 (2, 4) and (1, 6). Finally, we apply machine learning to our dataset in order to predict the orbifold geometry where a given particle spectrum can be found most likely.

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Moduli-dependent Calabi-Yau and SU(3)-structure metrics from Machine Learning

Cited by 5 publications

References 31 publications

Quantum Gravity and Phenomenology: Dark Matter, Dark Energy, Vacuum Selection, Emergent Spacetime, and Wormholes

Quantum Gravity and Phenomenology: Dark Matter, Dark Energy, Vacuum Selection, Emergent Spacetime, and Wormholes

Moduli-dependent KK towers and the swampland distance conjecture on the quintic Calabi-Yau manifold

The landscape of promising non-supersymmetric string models

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