Open mirror symmetry for pfaffian Calabi-Yau 3-folds

Shimizu, Mariko; Suzuki, Hisao

doi:10.1007/jhep03(2011)083

Cited by 15 publications

(24 citation statements)

References 60 publications

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“…We hope to return to some of these questions in a sequel. 15 Other useful references concerning mirror symmetry of non-complete intersection Calabi-Yau varieties include [27,47,48].…”

Section: Discussionmentioning

confidence: 99%

Nonabelian 2D gauge theories for determinantal Calabi-Yau varieties

Jockers¹,

Kumar

Lapan

et al. 2012

J. High Energ. Phys.

128

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The two-dimensional supersymmetric gauged linear sigma model (GLSM) with abelian gauge groups and matter fields has provided many insights into string theory on Calabi-Yau manifolds of a certain type: complete intersections in toric varieties. In this paper, we consider two GLSM constructions with nonabelian gauge groups and charged matter whose infrared CFTs correspond to string propagation on determinantal Calabi-Yau varieties, furnishing another broad class of Calabi-Yau geometries in addition to complete intersections. We show that these two models -which we refer to as the PAX and the PAXY model -are dual descriptions of the same low-energy physics. Using GLSM techniques, we determine the quantum Kähler moduli space of these varieties and find no disagreement with existing results in the literature.

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“…We hope to return to some of these questions in a sequel. 15 Other useful references concerning mirror symmetry of non-complete intersection Calabi-Yau varieties include [27,47,48].…”

Section: Discussionmentioning

confidence: 99%

Nonabelian 2D gauge theories for determinantal Calabi-Yau varieties

Jockers¹,

Kumar

Lapan

et al. 2012

J. High Energ. Phys.

128

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“…Motivated and guided by a number of works involving non-compact manifolds [6,7,8,9], a quantitative mirror correspondence involving D-branes on the quintic was established in [3]. Further works involving compact manifolds include [10,11,12,13,14,15,16,17,18]. In all these examples, the underlying manifold was selected from the beginning of the long and well-known list of complete intersections in toric varieties, for instance hypersurfaces in weighted projective spaces.…”

Section: Introductionmentioning

confidence: 99%

On the arithmetic of D-brane superpotentials: lines and conics on the mirror quintic

Walcher

2012

Communications in Number Theory and Physics

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Irrational invariants from D-brane superpotentials are pursued on the mirror quintic, systematically according to the degree of a representative curve. Lines are completely understood: the contribution from isolated lines vanishes. All other lines can be deformed holomorphically to the van Geemen lines, whose superpotential is determined via the associated inhomogeneous Picard-Fuchs equation. Substantial progress is made for conics: the families found by Mustaţǎ contain conics reducible to isolated lines, hence they have a vanishing superpotential. The search for all conics invariant under a residual Z 2 symmetry reduces to an algebraic problem at the limit of our computational capabilities. The main results are of arithmetic flavor: the extension of the moduli space by the algebraic cycle splits in the large complex structure limit into groups each governed by an algebraic number field. The expansion coefficients of the superpotential around large volume remain irrational. The integrality of those coefficients is revealed by a new, arithmetic twist of the di-logarithm: the D-logarithm. There are several options for attempting to explain how these invariants could arise from the A-model perspective. A successful spacetime interpretation will require spaces of BPS states to carry number theoretic structures, such as an action of the Galois group.

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“…Thus, we can interpret the seven-brane superpotential as a special case of the five-brane superpotential, where a description of the five-brane curve Σ in terms of seven-brane flux [F 2 ] = Σ is applicable [80], see also [100,120,121,123,[126][127][128][129] for a similar use of the seven-brane superpotential. 21 It is important to emphasize that the five-brane charge is only locally non-trivial, i.e.…”

Section: The Flux Superpotentialmentioning

confidence: 99%

“…For D5-branes in compact geometries the superpotential was calculated in [112,114,[116][117][118]122] by deriving and solving inhomogeneous Picard-Fuchs equations. Finally the methods of [110,111] have been extended to compact geometries in [115] and further applied in [120,121,[123][124][125][126][127][128][129].…”

Section: Chaptermentioning

confidence: 99%

Holomorphic couplings in non‐perturbative string compactifications

Klevers

2011

Fortschritte der Physik

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In this review article 1 we present an analysis of several aspects of four-dimensional, nonperturbative N = 1 compactifications of string theory. Our study focuses on brane dynamics and their effective physics as encoded in the holomorphic couplings of the low-energy N = 1 effective action, most prominently the superpotential W . This article is divided into three parts. In part one we derive the effective action of a spacetime-filling D5-brane in generic Type IIB Calabi-Yau orientifold compactifications. In the second part we invoke tools from string dualities, namely from F-theory, heterotic/F-theory duality and mirror symmetry, for a more elaborate study of the dynamics of (p, q) 7-branes and heterotic five-branes. In this context we perform exact computations of the complete perturbative effective superpotential, both due to branes and background fluxes. Finally, in the third part we present a novel geometric description of five-branes in Type IIB and heterotic M-theory Calabi-Yau compactifications via a non-Calabi-Yau threefoldẐ 3 , that is canonically constructed from the original fivebrane and the Calabi-Yau threefold Z 3 via a blow-up. We use the blow-up threefoldẐ 3 to derive open-closed Picard-Fuchs differential equations, that govern the complete effective brane and flux superpotential. In addition, we present first evidence to interpretẐ 3 as a flux compactification geometrically dual to the original five-brane by defining an SU (3)-structure onẐ 3 , that is generated dynamically by the five-brane backreaction.

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Open mirror symmetry for pfaffian Calabi-Yau 3-folds

Cited by 15 publications

References 60 publications

Nonabelian 2D gauge theories for determinantal Calabi-Yau varieties

Nonabelian 2D gauge theories for determinantal Calabi-Yau varieties

On the arithmetic of D-brane superpotentials: lines and conics on the mirror quintic

Holomorphic couplings in non‐perturbative string compactifications

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