Construction of mirror pairs Calabi-Yau orbifolds of the Berglund-Hubsch type
Abstract
In this paper we have developed general algorithm for finding all orbifolds of Berglund-Hubsch-type Calabi-Yau manifolds and their mirrors. An explicit construction is formulated for finding all admissible deformations and groups defining mirror pairs of orbifolds. Then using our algorithm for one of the Calabi-Yau manifolds, defined by a Fermat-type polynomial, we found all mirror pairs of orbifolds. For this model, for each pair of orbifolds, the number of generations and the number of singlets i.e. particles participating only in gravitational interactions (dark matter particles) were found.
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