Picard–Fuchs operators for octic arrangements, I: The case of orphans

Cynk, Sławomir; Straten, Duco van

doi:10.4310/cntp.2019.v13.n1.a1

Cited by 12 publications

(12 citation statements)

References 30 publications

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“…A further interesting class of examples to look at are Calabi-Yaus that do not have a point of maximal unipotent monodromy as discussed for instance in [30][31][32]. This would translate into GLSMs that do not have geometric phases.…”

Section: Discussionmentioning

confidence: 99%

GLSM realizations of maps and intersections of Grassmannians and Pfaffians

Căldăraru

Knapp

Sharpe

2018

J. High Energ. Phys.

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In this paper we give gauged linear sigma model (GLSM) realizations of a number of geometries not previously presented in GLSMs. We begin by describing GLSM realizations of maps including Veronese and Segre embeddings, which can be applied to give GLSMs explicitly describing non-complete intersection constructions such as the intersection of one hypersurface with the image under some map of another. We also discuss GLSMs for intersections of Grassmannians and Pfaffians with one another, and with their images under various maps, which sometimes form exotic constructions of Calabi-Yaus, as well as GLSMs for other exotic Calabi-Yau constructions of Kanazawa. Much of this paper focuses on a specific set of examples of GLSMs for intersections of Grassmannians G(2, N ) with themselves after a linear rotation, including the Calabi-Yau case N = 5. One phase of the GLSM realizes an intersection of two Grassmannians, the other phase realizes an intersection of two Pfaffians. The GLSM has two nonabelian factors in its gauge group, and we consider dualities in those factors. In both the original GLSM and a double-dual, one geometric phase is realized perturbatively (as the critical locus of a superpotential), and the other via quantum effects. Dualizing on a single gauge group factor yields a model in which each geometry is realized through a simultaneous combination of perturbative and quantum effects.

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Section: Discussionmentioning

confidence: 99%

GLSM realizations of maps and intersections of Grassmannians and Pfaffians

Căldăraru

Knapp

Sharpe

2018

J. High Energ. Phys.

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“…Seven explicit examples of this situation are described in ref. [123]: they corresponds to the resolved double octics arising from the Meyer arrangements of eight lines [108] Quantum-consistent 'magic' cubic pre-potentials. The Calabi-Yau manifolds which are finite quotients of either an Abelian variety A or a product of a K3 surface with an elliptic curve [55], have cubic pre-potentials corresponding to arithmetic quotients of the reducible symmetric special geometry…”

Section: Jhep09(2020)147mentioning

confidence: 99%

Special geometry and the swampland

Cecotti

2020

J. High Energ. Phys.

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In the context of 4d effective gravity theories with 8 supersymmetries, we propose to unify, strenghten, and refine the several swampland conjectures into a single statement: the structural criterion, modelled on the structure theorem in Hodge theory. In its most abstract form the new swampland criterion applies to all 4d $$ \mathcal{N} $$ N = 2 effective theories (having a quantum-consistent UV completion) whether supersymmetry is local or rigid: indeed it may be regarded as the more general version of Seiberg-Witten geometry which holds both in the rigid and local cases. As a first application of the new swampland criterion we show that a quantum-consistent $$ \mathcal{N} $$ N = 2 supergravity with a cubic pre-potential is necessarily a truncation of a higher-$$ \mathcal{N} $$ N sugra. More precisely: its moduli space is a Shimura variety of ‘magic’ type. In all other cases a quantum-consistent special Kähler geometry is either an arithmetic quotient of the complex hyperbolic space SU(1, m)/U(m) or has no local Killing vector. Applied to Calabi-Yau 3-folds this result implies (assuming mirror symmetry) the validity of the Oguiso-Sakurai conjecture in Algebraic Geometry: all Calabi-Yau 3-folds X without rational curves have Picard number ρ = 2, 3; in facts they are finite quotients of Abelian varieties. More generally: the Kähler moduli of X do not receive quantum corrections if and only if X has infinite fundamental group. In all other cases the Kähler moduli have instanton corrections in (essentially) all possible degrees.

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“…For example in [16] the so-called Calabi-Yau operators, which provide an abstract version of Picard-Fuchs operators, are required to have a MUM point. Nevertheless, there are numerous examples of Picard-Fuchs operators which do not have a MUM point (see [9]). In general, it is not clear how to approach the construction of rational basis in those cases.…”

Section: Local Monodromy Operatorsmentioning

confidence: 99%

Coefficients of the monodromy matrices of one-parameter families of double octic Calabi-Yau threefolds at a half-conifold point

Chmiel¹

2021

Preprint

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Doran and Morgan introduced in [10] a rational basis for the monodromy group of the Picard-Fuchs operator of a hypergeometric family of Calabi-Yau threefolds. In this paper we compute numerically the transition matrix between a generalization of the Doran-Morgan basis and the Frobenius basis at a half-conifold point of a one-parameter family of double octic Calabi-Yau threefolds. We identify the entries of this matrix as rational functions in the special values L(f, 1) and L(f, 2) of the corresponding modular form f and one constant. We also present related results concerning the rank of the group of period integrals generated by the action of the monodromy group on the conifold period.

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Picard–Fuchs operators for octic arrangements, I: The case of orphans

Cited by 12 publications

References 30 publications

GLSM realizations of maps and intersections of Grassmannians and Pfaffians

GLSM realizations of maps and intersections of Grassmannians and Pfaffians

Special geometry and the swampland

Coefficients of the monodromy matrices of one-parameter families of double octic Calabi-Yau threefolds at a half-conifold point

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