Mirror symmetry for toric branes on compact hypersurfaces

Alim, Murad; Hecht, Michael; Mayr, Peter; Mertens, Adrian

doi:10.1088/1126-6708/2009/09/126

Cited by 47 publications

(250 citation statements)

References 48 publications

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“…There are many other works on periods in heterotic/F -theory duality. For more computational approaches, see for example [49,50,36,51,52,53,54,55,56,57].…”

Section: Thus We Havementioning

confidence: 99%

Weak Coupling, Degeneration and Log Calabi-Yau Spaces

Donagi

Katz

Wijnholt

2013

Pure and Applied Mathematics Quarterly

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Abstract:We establish a new weak coupling limit in F -theory. The new limit may be thought of as the process in which a local model bubbles off from the rest of the Calabi-Yau. The construction comes with a small deformation parameter t such that computations in the local model become exact as t → 0. More generally, we advocate a modular approach where compact Calabi-Yau geometries are obtained by gluing together local pieces (log Calabi-Yau spaces) into a normal crossing variety and smoothing, in analogy with a similar cutting and gluing approach to topological field theories. We further argue for a holographic relation between F -theory on a degenerate Calabi-Yau and a dual theory on its boundary, which fits nicely with the gluing construction.

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“…There are many other works on periods in heterotic/F -theory duality. For more computational approaches, see for example [49,50,36,51,52,53,54,55,56,57].…”

Section: Thus We Havementioning

confidence: 99%

Weak Coupling, Degeneration and Log Calabi-Yau Spaces

Donagi

Katz

Wijnholt

2013

Pure and Applied Mathematics Quarterly

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“…Alternatively, we can directly take the limit of (Z 3 , Z 3 ) to the non-compact geometry in a Type II description where similar results can be obtained, cf. also [120,123].…”

Section: Constructing Elliptic Fourfolds: Strategymentioning

confidence: 97%

“…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%

“…In this context the connection of the fourfold geometry ∆X 5 with the brane charge vectors can be understood as a consequence of heterotic/F-theory duality [82]. We note that adding this vector to form a higher-dimensional non-reflexive polyhedron was first proposed in [109,120,268] in the context of the B-model and then extended to the compact case in [100,127], where a connection with heterotic/F-theory duality was exploited.…”

Section: The Elliptically Fibered Calabi-yau Fourfoldmentioning

confidence: 99%

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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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“…But since open string amplitudes W i0...i k are only cyclically symmetric, only a non-commutative W ∞ can encode all information on the W i0...i k . 3 The topological metric has ghost number 3 and hence induces non-degenerate pairings Ext written as…”

Section: Introductionmentioning

confidence: 99%

Remarks on quiver gauge theories from open topological string theory

Carqueville

Velez

2010

J. High Energ. Phys.

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We study effective quiver gauge theories arising from a stack of D3-branes on certain Calabi-Yau singularities. Our point of view is a first principle approach via open topological string theory. This means that we construct the natural A ∞ -structure of open string amplitudes in the associated D-brane category. Then we show that it precisely reproduces the results of the method of brane tilings, without having to resort to any effective field theory computations. In particular, we prove a general and simple formula for effective superpotentials.

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Mirror symmetry for toric branes on compact hypersurfaces

Cited by 47 publications

References 48 publications

Weak Coupling, Degeneration and Log Calabi-Yau Spaces

Weak Coupling, Degeneration and Log Calabi-Yau Spaces

Holomorphic couplings in non‐perturbative string compactifications

Remarks on quiver gauge theories from open topological string theory

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