Review on Special Geometry and Mirror Symmetry for Calabi-Yau Manifolds (Brief Review)
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 $N = 1$ 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 $N = 2$ Superconformal Field theory with the central charge $c = 9$. Each of these two equivalent approaches has its own merits. Say, using exactly solvability of the Minimal models of $N = 2$ 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 $N = 2$ superconformal minimal models and with supersymmetric gauged linear sigma models.
- Publication:
-
Soviet Journal of Experimental and Theoretical Physics Letters
- Pub Date:
- November 2023
- DOI:
- 10.1134/S0021364023603147
- Bibcode:
- 2023JETPL.118..701B