Machine learning line bundle connections by Anthony Ashmore, Rehan Deen, Yang-Hui He, Burt A. Ovrut

“…We study the use of machine learning for finding numerical hermitian Yang–Mills connections on line bundles over Calabi–Yau manifolds. Defining an appropriate loss function and focusing on the examples of an elliptic curve, a K3 surface and a quintic threefold, we show that neural networks can be trained to give a close approximation to hermitian Yang–Mills connections.…”
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On flux vacua and modularity by Rolf Schimmrigk

“…The analysis of some Calabi-Yau manifolds which do not admit supersymmetric flux vacua shows that the reverse of the conjecture does not hold.…”
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Hyperconifold Transitions, Mirror Symmetry, and String Theory by Davies, R

“…The new hyperconifold transitions are also used to construct a small number of new Calabi-Yau manifolds, with small Hodge numbers and fundamental group Z_3 or Z_5. …”

Singularities of special Lagrangian submanifolds by Joyce, D

“…We survey what is known about singularities of special Lagrangian submanifolds (SL $m$-folds) in (almost) Calabi-Yau manifolds. The bulk of the paper summarizes the author's work [18-22] on SL $m$-folds $X$ with isolated conical singularities. …”

ROLLING AMONG CALABI-YAU VACUA by Candelas, P, Green, P, Hubsch, T

“…For a very large number of Calabi-Yau manifolds of many different numerical invariants and hence distinct homotopy types, the relevant moduli spaces can be assembled into a connected web. …”

Integrality structures in topological strings and quantum 2-functions by Shengmao Zhu

“…Abstract In this article, we first prove the integrality of an explicit disc counting formula obtained by Panfil and Sulkowski for a class of toric Calabi-Yau manifolds named generalized conifolds. Then, motivated by the integrality structures in open topological string theory, we introduce a mathematical notion of “quantum 2-function” which can be viewed as the quantization of the notion of “2-function” introduced by Schwarz, Vologod-sky and Walcher. …”
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Variations of Hodge Structure Considered as an Exterior Differential System: Old and New Results by James Carlson, Mark Green, Phillip Griffiths

“…The paper ends with some speculation on EDS and Hodge conjecture for Calabi-Yau manifolds.…”
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Type IIB flux compactifications with h 1,1 = 0 by Jacob Bardzell, Eduardo Gonzalo, Muthusamy Rajaguru, Danielle Smith, Timm Wrase

“…Abstract We revisit flux compactifications of type IIB string theory on ‘spaces’ dual to rigid Calabi-Yau manifolds. This rather unexplored part of the string landscapes harbors many interesting four-dimensional solutions, namely supersymmetric N $$ \mathcal{N} $$ = 1 Minkowski vacua without flat direction and infinite families of AdS vacua, some potentially with unrestricted rank for the gauge group. …”
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A Generalized Construction of Calabi-Yau Models and Mirror Symmetry by Per Berglund, Tristan Hubsch

“…We extend the construction of Calabi-Yau manifolds to hypersurfaces in non-Fano toric varieties, requiring the use of certain Laurent defining polynomials, and explore the phases of the corresponding gauged linear sigma models. …”
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Tops as building blocks for G 2 manifolds by Andreas P. Braun

“…These building blocks, which are appropriate K3-fibred threefolds, are shown to have a natural and elegant construction in terms of tops, which parallels the construction of Calabi-Yau manifolds via reflexive polytopes. In particular, this enables us to prove combinatorial formulas for the Hodge numbers and other relevant topological data.…”
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(2, 2) geometry from gauge theory by João Caldeira, Travis Maxfield, Savdeep Sethi

“…Abstract Using gauge theory, we describe how to construct generalized Kähler geometries with (2, 2) two-dimensional supersymmetry, which are analogues of familiar examples like projective spaces and Calabi-Yau manifolds. For special cases, T-dual descriptions can be found which are squashed Kähler spaces. …”
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Renormalization Method and Mirror Symmetry by Si Li

“…We analyze Givental's symplectic loop space formalism in the context of B-model geometry on Calabi-Yau manifolds, and explain the Fock space construction via the renormalization techniques of gauge theory. …”
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Tops as building blocks for G2 manifolds by Braun, A

“…These building blocks, which are appropriate K3-fibred threefolds, are shown to have a natural and elegant construction in terms of tops, which parallels the construction of Calabi-Yau manifolds via reflexive polytopes. In particular, this enables us to prove combinatorial formulas for the Hodge numbers and other relevant topological data.…”

Singularities of special Lagrangian submanifolds by Joyce, D

“…We survey what is known about singularities of special Lagrangian submanifolds (SL m-folds) in (almost) Calabi-Yau manifolds. The bulk of the paper summarizes the author's five papers math.DG/0211294, math.DG/0211295, math.DG/0302355, math.DG/0302356, math.DG/0303272 on SL m-folds X with isolated conical singularities. …”

Classification of base geometries in F-theory by Wang, Yinan, Ph. D. Massachusetts Institute of Technology

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Heterotic compactification, an algorithmic approach by Anderson, L, He, Y, Lukas, A

“…This is done in the context of complete intersection Calabi-Yau manifolds in a single projective space where we classify positive monad bundles. …”

Non-perturbative topological string theory on compact Calabi-Yau 3-folds by Jie Gu, Amir-Kian Kashani-Poor, Albrecht Klemm, Marcos Mariño

“…We obtain analytic and numerical results for the non-perturbative amplitudes of topological string theory on arbitrary, compact Calabi-Yau manifolds. Our approach is based on the theory of resurgence and extends previous special results to the more general case. …”
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Neural network approximations for Calabi-Yau metrics by Vishnu Jejjala, Damián Kaloni Mayorga Peña, Challenger Mishra

“…This investigation employs a simple, modular neural network architecture that is capable of approximating Ricci flat Kähler metrics for Calabi-Yau manifolds of dimensions two and three. We show that measures that assess the Ricci flatness and consistency of the metric decrease after training. …”
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Yukawa textures from singular spectral data by Mohsen Karkheiran

“…We only work with Weierstrass elliptically fibered Calabi-Yau manifolds here. The idea for generalizing this approach to every elliptically fibered Calabi-Yau with rational sections is given at the end of this paper.…”
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Affine characters at negative level and elliptic genera of non-critical strings by David Jaramillo Duque, Amir-Kian Kashani-Poor

“…We formulate a general ansatz for these in terms of characters of the affine Lie algebra associated to the 6d gauge group at negative level, and provide ample evidence for the validity of this ansatz for 6d theories obtained via F-theory compactification on elliptically fibered Calabi-Yau manifolds over a Hirzebruch base. We obtain novel closed form results for many elliptic genera in terms of our ansatz, and show that our results specialize consistently when moving along Higgsing trees.…”
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