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- Title
Review on Special Geometry and Mirror Symmetry for Calabi–Yau Manifolds (Brief Review).
- Authors
Belavin, A.; Eremin, B.; Parkhomenko, S.
- Abstract
Ten-dimensional Superstring theory unifies the Standard Model of the strong, electromagnetic, and weak interactions with quantum gravity. Starting with 10-dimensional superstring theory, we can get a 4-dimensional theory with spacetime supersymmetry following the Kaluza–Klein idea by compactifying six of the ten dimensions. For phenomenological reasons we need to do this while maintaining Supersymmetry of 4-dimensional spacetime. To achieve this, as Candelas, Horowitz, Strominger, and Witten [1] have shown, we must compactify six of the ten dimensions of to the so called Calabi–Yau manifolds. Another equivalent approach developed by D. Gepner [2, 3] is the compactification of 6 dimensions onto some Superconformal Field theory with the central charge . Each of these two equivalent approaches has its own merits. Say, using exactly solvability of the Minimal models of Superconformal Field Theory, it is possible to obtain the explicit solution of the considered models. In this article we review a series of our works on Calabi–Yau manifolds, their mirror symmetry, special geometry on the moduli space of Calabi–Yau, the connection of Calabi–Yau manifolds with superconformal minimal models and with supersymmetric gauged linear sigma models.
- Subjects
CALABI-Yau manifolds; MIRROR symmetry; SUPERSYMMETRY; SUPERSTRING theories; QUANTUM gravity; GEOMETRY
- Publication
JETP Letters, 2023, Vol 118, Issue 10, p701
- ISSN
0021-3640
- Publication type
Article
- DOI
10.1134/S0021364023603147