scholarly journals The Arithmetic Mirror Symmetry and¶Calabi-Yau Manifolds

2000 ◽  
Vol 210 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Valeri A. Gritsenko ◽  
Viacheslav V. Nikulin
Keyword(s):  
Mirror Symmetry ◽  
Calabi Yau Manifolds

scholarly journals On the supergravity formulation of mirror symmetry in generalized Calabi–Yau manifolds

2007 ◽  
Vol 780 (1-2) ◽  
pp. 28-39 ◽  
Author(s):  
R. D'Auria ◽  
S. Ferrara ◽  
M. Trigiante
Keyword(s):  
Mirror Symmetry ◽  
Calabi Yau Manifolds

Mathematics for string phenomenology

2015 ◽  
Vol 30 (03) ◽  
pp. 1530018
Author(s):  
Michael R. Douglas
Keyword(s):  
Mirror Symmetry ◽  
Complex Structure ◽  
Toric Geometry ◽  
Mathematical Ideas ◽  
String Phenomenology ◽  
Calabi Yau Manifolds

We survey some of the basic mathematical ideas and techniques which are used in string phenomenology, such as constructions of Calabi–Yau manifolds, singularities and orbifolds, toric geometry, variation of complex structure, and mirror symmetry.

scholarly journals Erratum to "SYZ mirror symmetry for toric Calabi-Yau manifolds"

2015 ◽  
Vol 99 (1) ◽  
pp. 165-167
Author(s):  
Kwokwai Chan ◽  
Siu-Cheong Lau ◽  
Naichung Conan Leung
Keyword(s):  
Mirror Symmetry ◽  
Calabi Yau Manifolds

scholarly journals MIRROR SYMMETRY AND STRING VACUA FROM A SPECIAL CLASS OF FANO VARIETIES

1996 ◽  
Vol 11 (17) ◽  
pp. 3049-3096 ◽  
Author(s):  
ROLF SCHIMMRIGK
Keyword(s):  
Chern Class ◽  
Mirror Symmetry ◽  
Central Charge ◽  
Mean Field ◽  
Fano Varieties ◽  
Complex Dimension ◽  
Crucial Information ◽  
First Chern Class ◽  
The One ◽  
Calabi Yau Manifolds

Because of the existence of rigid Calabi-Yau manifolds, mirror symmetry cannot be understood as an operation on the space of manifolds with vanishing first Chern class. In this article I continue to investigate a particular type of Kähler manifolds with positive first Chern class which generalize Calabi-Yau manifolds in a natural way and which provide a framework for mirrors of rigid string vacua. This class comprises Fano manifolds of a special type which encode crucial information about ground states of the superstring. It is shown in particular that the massless spectra of (2, 2)-supersymmetric vacua of central charge ĉ=D crit can be derived from special Fano varieties of complex dimension D crit +2(Q−1), Q>1, and that in certain circumstances it is even possible to embed Calabi-Yau manifolds into such higher dimensional spaces. The constructions described here lead to new insight into the relation between exactly solvable models and their mean field theories on the one hand and their corresponding Calabi-Yau manifolds on the other. Furthermore it is shown that Witten’s formulation of the Landau-Ginzburg/Calabi-Yau relation can be applied to the present framework as well.

scholarly journals SYZ mirror symmetry for toric Calabi-Yau manifolds

2012 ◽  
Vol 90 (2) ◽  
pp. 177-250 ◽  
Author(s):  
Kwokwai Chan ◽  
Siu-Cheong Lau ◽  
Naichung Conan Leung
Keyword(s):  
Mirror Symmetry ◽  
Calabi Yau Manifolds

scholarly journals A Generalized Construction of Calabi-Yau Models and Mirror Symmetry

2018 ◽  
Vol 4 (2) ◽  
Author(s):  
Per Berglund ◽  
Tristan Hubsch
Keyword(s):  
Sigma Models ◽  
General Class ◽  
Mirror Symmetry ◽  
Original Work ◽  
Convex Polytopes ◽  
Toric Varieties ◽  
Linear Sigma Models ◽  
Calabi Yau Manifolds

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. The associated non-reflexive and non-convex polytopes provide a generalization of Batyrev’s original work, allowing us to construct novel pairs of mirror models. We showcase our proposal for this generalization by examining Calabi-Yau hypersurfaces in Hirzebruch n-folds, focusing on n=3,4 sequences, and outline the more general class of so-defined geometries.

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