Abstract
Two constructions of mirror pairs of Calabi-Yau manifolds are compared by example of quintic orbifolds \(\mathcal{Q}\). The first, Berglund—Hubsch—Krawitz, construction is as follows. If X is the factor of the hypersurface \(\mathcal{Q}\) by a certain subgroup H′ of the maximum allowed group SL, the mirror manifold Y is defined as the factor by the dual subgroup H,′T. In the second, Batyrev, construction, the toric manifold T containing the mirror Y as a hypersurface specified by zeros of the polynomial WY is determined from the properties of the polynomial WX specifying the Calabi-Yau manifold X. The polynomial WY is determined in an explicit form. The group of symmetry of the polynomial WY is found from its form and it is tested whether it coincides with that predicted by the Berglund—Hubsch—Krawitz construction.
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We are grateful to A. Litvinov for stimulating discussions.
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Russian Text © The Author(s), 2020, published in Pis’ma v Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2020, Vol. 112, No. 6, pp. 388–393.
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This work was performed at the Landau Institute for Theoretical Physics, Russian Academy of Sciences. A. Belavin acknowledges the support of the Ministry of Science and Higher Education of the Russian Federation (state assignment no. 0033-2019-0004). B. Eremin acknowledges the support of the Russian Science Foundation (project no. 18-12-00439).
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Belavin, A., Eremin, B. Mirror Pairs of Quintic Orbifolds. Jetp Lett. 112, 370–375 (2020). https://doi.org/10.1134/S002136402018006X
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DOI: https://doi.org/10.1134/S002136402018006X