Mirror Symmetry, Mirror Map and Applications to Calabi-Yau Hypersurfaces
S. Hosono (1), A. Klemm (2), S. Theisen (2), S.-T. Yau (1) ((1) Dept., of Mathematics, Harvard University; (2) Sektion Physik der Universit\"at, M\"unchen)
TL;DR
This paper explores mirror symmetry in Calabi-Yau hypersurfaces using toric geometry, providing explicit mirror maps and Yukawa couplings for multiple examples, thereby advancing understanding of mirror pairs and their properties.
Contribution
It introduces a toric geometry framework to establish mirror symmetry for Calabi-Yau spaces previously lacking known mirrors, with explicit calculations of mirror maps and Yukawa couplings.
Findings
Mirror symmetry established for new Calabi-Yau examples
Explicit mirror maps provided for cases with two and three moduli
Yukawa couplings computed explicitly for these examples
Abstract
Mirror Symmetry, Picard-Fuchs equations and instanton corrected Yukawa couplings are discussed within the framework of toric geometry. It allows to establish mirror symmetry of Calabi-Yau spaces for which the mirror manifold had been unavailable in previous constructions. Mirror maps and Yukawa couplings are explicitly given for several examples with two and three moduli.
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