Machine Learning Calabi–Yau Metrics

Ashmore, Anthony; He, Yang‐Hui; Ovrut, Burt A.

doi:10.1002/prop.202000068

Cited by 57 publications

(45 citation statements)

References 68 publications

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“…Finally, the immense size of discrete data sets in string theory, such as those encountered here, suggests the use of data science techniques — see [4–25] as well as the reviews [26] and [27]. In the final part of this work, we develop machine learning algorithms to predict the topological data of Calabi‐Yau threefolds.…”

Section: Introductionmentioning

confidence: 99%

Bounding the Kreuzer‐Skarke Landscape

Demirtaş

McAllister

Rios-Tascon

2020

Fortschritte der Physik

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We study Calabi-Yau threefolds with large Hodge numbers by constructing and counting triangulations of reflexive polytopes. By counting points in the associated secondary polytopes, we show that the number of fine, regular, star triangulations of polytopes in the Kreuzer-Skarke list is bounded above by (14,111 494) ≈ 10 928. Adapting a result of Anclin on triangulations of lattice polygons, we obtain a bound on the number of triangulations of each 2-face of each polytope in the list. In this way we prove that the number of topologically inequivalent Calabi-Yau hypersurfaces arising from the Kreuzer-Skarke list is bounded above by 10 428. We introduce efficient algorithms for constructing representative ensembles of Calabi-Yau hypersurfaces, including the extremal case h 1,1 = 491, and we study the distributions of topological and physical data therein. Finally, we demonstrate that neural networks can accurately predict these data once the triangulation is encoded in terms of the secondary polytope.

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Section: Introductionmentioning

confidence: 99%

Bounding the Kreuzer‐Skarke Landscape

Demirtaş

McAllister

Rios-Tascon

2020

Fortschritte der Physik

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“…But how does one know for sure and what does one say if the coefficients are simply generic looking, seemingly innocuous, values? In this paper we wish to show that modern numerical methods for determining Ricci-flat metrics on Calabi-Yau manifolds [9][10][11][12][13][14][15][16][17][18] are a practical and efficient tool for deciding such questions in many cases.…”

Section: Jhep05(2020)044mentioning

confidence: 99%

“…In this section we briefly review some of the existing methods for obtaining numerical approximations to Ricci-flat metrics on Calabi-Yau manifolds [9][10][11][12][13][14][15][16][17][18]. This is an evolving field with new techniques still being developed, notably recently including methods from Machine Learning [18] (related work on Machine Learning and more general metrics with SU(3) structure is currently underway [19]). In this section, however, we will focus on the approach of [15] which is the methodology which will be employed in this paper.…”

Section: Numerical Computationmentioning

confidence: 99%

Numerical metrics, curvature expansions and Calabi-Yau manifolds

Cui

Gray

2020

J. High Energ. Phys.

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We discuss the extent to which numerical techniques for computing approximations to Ricci-flat metrics can be used to investigate hierarchies of curvature scales on Calabi-Yau manifolds. Control of such hierarchies is integral to the validity of curvature expansions in string effective theories. Nevertheless, for seemingly generic points in moduli space it can be difficult to analytically determine if there might be a highly curved region localized somewhere on the Calabi-Yau manifold. We show that numerical techniques are rather efficient at deciding this issue.

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“…Unfortunately, this would require the inclusion of normalization considerations arising from the matter field Kähler potential and this object is extremely difficult to compute. Some approximations to the Kähler potential do exist in the literature [17][18][19][20][21], and its computation is the ultimate goals of much of the work on numerical approaches to Ricci-flat metrics and gauge bundle connections on Calabi-Yau manifolds [22][23][24][25][26][27][28][29][30][31][32][33][34][35]. Nevertheless, it is fair to say that there is still very little known about the physically normalized Yukawa couplings.…”

Section: Introductionmentioning

confidence: 99%

Generalized vanishing theorems for Yukawa couplings in heterotic compactifications

Anderson

Gray

Larfors

et al. 2021

J. High Energ. Phys.

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Heterotic compactifications on Calabi-Yau threefolds frequently exhibit textures of vanishing Yukawa couplings in their low energy description. The vanishing of these couplings is often not enforced by any obvious symmetry and appears to be topological in nature. Recent results used differential geometric methods to explain the origin of some of this structure [1, 2]. A vanishing theorem was given which showed that the effect could be attributed, in part, to the embedding of the Calabi-Yau manifolds of interest inside higher dimensional ambient spaces, if the gauge bundles involved descended from vector bundles on those larger manifolds. In this paper, we utilize an algebro-geometric approach to provide an alternative derivation of some of these results, and are thus able to generalize them to a much wider arena than has been considered before. For example, we consider cases where the vector bundles of interest do not descend from bundles on the ambient space. In such a manner we are able to highlight the ubiquity with which textures of vanishing Yukawa couplings can be expected to arise in heterotic compactifications, with multiple different constraints arising from a plethora of different geometric features associated to the gauge bundle.

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Machine Learning Calabi–Yau Metrics

Cited by 57 publications

References 68 publications

Bounding the Kreuzer‐Skarke Landscape

Bounding the Kreuzer‐Skarke Landscape

Numerical metrics, curvature expansions and Calabi-Yau manifolds

Generalized vanishing theorems for Yukawa couplings in heterotic compactifications

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