String dualities and toric geometry: an introduction
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In this paper, the concepts of toric geometry that are necessary to understand applications in the context of string and F-theory dualities have been introduced, based on the definition of a toric variety in terms of homogeneous coordinates.Abstract:
This note is supposed to be an introduction to those concepts of toric geometry that are necessary to understand applications in the context of string and F-theory dualities The presentation is based on the definition of a toric variety in terms of homogeneous coordinates, stressing the analogy with weighted projective spaces We try to give both intuitive pictures and precise rules that should enable the reader to work with the concepts presented hereread more
Citations
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Journal ArticleDOI
D-branes at del Pezzo singularities: global embedding and moduli stabilisation
Michele Cicoli,Sven Krippendorf,Christoph Mayrhofer,Fernando Quevedo,Fernando Quevedo,Roberto Valandro +5 more
TL;DR: In this article, the authors combine moduli stabilisation and model building on branes at del Pezzo singularities in a fully consistent global compactification of Calabi-Yau manifolds.
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Localized Tachyons and RG Flows
TL;DR: In this paper, the authors studied condensation of closed string tachyons living on defects, such as orbifold fixed planes and Neveu-Schwarz fivebranes.
Journal ArticleDOI
Global F-theory models: instantons and gauge dynamics
Mirjam Cvetič,Mirjam Cvetič,Iñaki García-Etxebarria,Iñaki García-Etxebarria,James Halverson,James Halverson +5 more
TL;DR: In this paper, a compact F-theory GUT model is presented, in which D-brane instantons generate the top Yukawa coupling non-perturbatively.
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Lectures on complex geometry, Calabi-Yau manifolds and toric geometry
TL;DR: In this article, the authors define basic concepts of complex and Kahler geometry, and then proceed with an analysis of various definitions of Calabi-Yau manifolds, and provide a short introduction to toric geometry, aimed at constructing CYF in two different ways: as hypersurfaces in toric varieties and as local toric CalabiYau threefolds.
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Toric K3-fibred Calabi-Yau manifolds with del Pezzo divisors for string compactifications
TL;DR: In this paper, the authors analyse several explicit toric examples of compact K3-fibred Calabi-Yau three-folds and show that they can be used for the study of string dualities and are crucial ingredients for the construction of LARGE Volume type IIB vacua with promising applications to cosmology and particle phenomenology.
References
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Book
Principles of Algebraic Geometry
Phillip Griffiths,Joe Harris +1 more
TL;DR: In this paper, a comprehensive, self-contained treatment of complex manifold theory is presented, focusing on results applicable to projective varieties, and including discussion of the theory of Riemann surfaces and algebraic curves, algebraic surfaces and the quadric line complex.
Book
Introduction to Toric Varieties.
TL;DR: In this article, a mini-course is presented to develop the foundations of the study of toric varieties, with examples, and describe some of these relations and applications, concluding with Stanley's theorem characterizing the number of simplicies in each dimension in a convex simplicial polytope.
Journal ArticleDOI
String theory dynamics in various dimensions
TL;DR: The strong coupling dynamics of string theories in dimension d ⩾ 4 are studied in this paper, where it is argued that eleven-dimensional supergravity arises as a low energy limit of the ten-dimensional Type IIA superstring.
Journal ArticleDOI
Phases of N = 2 theories in two dimensions
TL;DR: In this paper, a natural relation between sigma models based on Calabi-Yau hypersurfaces in weighted projective spaces and Landau-Ginzburg models is found.
Journal ArticleDOI
Unity of superstring dualities
Chris Hull,Paul K. Townsend +1 more
TL;DR: In this article, it was shown that the effective action for type II string theory compactified on a six-torus is N = 8 supergravity, which is known to have an E7 duality symmetry.
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