Numerical metrics for complete intersection and Kreuzer–Skarke Calabi–Yau manifolds

Larfors, Magdalena; Lukas, André; Ruehle, Fabian; Schneider, Robin

doi:10.1088/2632-2153/ac8e4e

Cited by 18 publications

(8 citation statements)

References 48 publications

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“…In another direction, rather than solving these systems by flowing, one might simply solve the equation for the dilaton using some other method, such as by using a neural network to parametrise ϕ and then minimising a loss function which encodes the Bianchi identity. This approach has been used recently for finding numerical Calabi-Yau metrics [102][103][104][105][106][107][108] and hermitian Yang-Mills connections [109], and is likely to be a powerful technique for solving non-linear PDEs in the future.…”

Section: Numerical Approximations To Non-kähler Metricsmentioning

confidence: 99%

Geometric flows and supersymmetry

Ashmore¹,

Minasian²,

Proto³

2023

Preprint

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We study the relation between supersymmetry and geometric flows driven by the Bianchi identity for the three-form flux H in heterotic supergravity. We describe how the flow equations can be derived from a functional that appears in a rewriting of the bosonic action in terms of squares of supersymmetry operators.On a complex threefold, the resulting equations match what is known in the mathematics literature as "anomaly flow". We generalise this to seven-and eightmanifolds with G 2 or Spin(7) structures and discuss examples where the manifold is a torus fibration over a K3 surface. In the latter cases, the flow simplifies to a single scalar equation, with the existence of the supergravity solution implied by the long-time existence and convergence of the flow. We also comment on the α ′ expansion and highlight the importance of using the proper connection in the Bianchi identity to ensure that the flow's fixed points satisfy the supergravity equations of motion.

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Section: Numerical Approximations To Non-kähler Metricsmentioning

confidence: 99%

Geometric flows and supersymmetry

Ashmore¹,

Minasian²,

Proto³

2023

Preprint

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“…We will consider the complete intersection Calabi-Yau manifold (CICY). The Monte-Carlo integration over CICYs has been studied in [39,40,48,49,52]. We will closely follow them in this subsection 3 .…”

Section: Numerical Integration Over Calabi-yau Threefoldmentioning

confidence: 99%

“…In recent years, several numerical methods are developed to solve this problem for example the (generalized) Donaldson algorithm [38][39][40][41][42][43], minimization algorithm [44][45][46] and more recently machine learning algorithms [47][48][49][50][51][52][53][54][55][56]. By them, one can compute the RFM of a CY manifold and the HYM connection of a poly-stable bundle to a high degree of accuracy.…”

Section: Introductionmentioning

confidence: 99%

Numerical Hermitian Yang-Mills Connection for Bundles on Quotient Manifold

Cui¹

2023

Preprint

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We extend the previous computations of Hermitian Yang-Mills connections for bundles on complete intersection Calabi-Yau manifolds to bundles on their free quotients. Bundles on quotient manifolds are often defined by equivariant bundles on corresponding covering spaces. Combining equivariant structure and generalized Donaldson's algorithm, we develop a systematic approach to compute connections of holomorphic poly-stable bundles on quotient manifolds. With it, we construct the connections of an SU (3) bundle on Z 5 quotient of quintic and an SU (5) bundle on Z 3 × Z 3 quotient of Bi-cubic. For both of these examples, the algorithm converges as expected and gives a good approximation of Hermitian Yang-Mills connections, which will be important for heterotic model building in Calabi-Yau compactification.

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“…This calls for new point generators and a new training loop. Such point generating algorithms have been developed for CICY manifolds [BBDO08a] and CY manifolds in toric ambient spaces [LLRS21,LLRS22]. They are direct generalisations of the homogeneous sampling technique described for the Quintic sin section 4, and are included in the cymetric package's point generator routines.…”

Section: Machine Learning Experiments Beyond the Quinticmentioning

confidence: 99%

Moduli-dependent Calabi-Yau and SU(3)-structure metrics from machine learning

Anderson

Gerdes²,

Gray

et al. 2021

J. High Energ. Phys.

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We use machine learning to approximate Calabi-Yau and SU(3)-structure metrics, including for the first time complex structure moduli dependence. Our new methods furthermore improve existing numerical approximations in terms of accuracy and speed. Knowing these metrics has numerous applications, ranging from computations of crucial aspects of the effective field theory of string compactifications such as the canonical normalizations for Yukawa couplings, and the massive string spectrum which plays a crucial role in swampland conjectures, to mirror symmetry and the SYZ conjecture. In the case of SU(3) structure, our machine learning approach allows us to engineer metrics with certain torsion properties. Our methods are demonstrated for Calabi-Yau and SU(3)-structure manifolds based on a one-parameter family of quintic hypersurfaces in ℙ4.

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Numerical metrics for complete intersection and Kreuzer–Skarke Calabi–Yau manifolds

Cited by 18 publications

References 48 publications

Geometric flows and supersymmetry

Geometric flows and supersymmetry

Numerical Hermitian Yang-Mills Connection for Bundles on Quotient Manifold

Moduli-dependent Calabi-Yau and SU(3)-structure metrics from machine learning

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