Abstract
The Kähler potentials have been calculated on the moduli space of complex structures for two Calabi-Yau manifolds specified as hypersurfaces in weighted projective spaces. Mirror images of these manifolds have been found according to the Batyrev and Berglund—Hübsch constructions and their equivalence has been demonstrated.
Similar content being viewed by others
References
P. Candelas, G. T. Horowitz, A. Strominger, and E. Witten, Nucl. Phys. B 258, 46 (1985). https://doi.org/10.1016/0550-3213(85)90602-9
P. Berglund and T. Hübsch, Nucl. Phys. B 393, 377 (1993); arXiv: hep-th/9201014 [hep-th]. https://doi.org/10.1016/0550-3213(93)90250-s
K. Aleshkin and A. Belavin, JETP Lett. 108, 705 (2018); aXiv: 1806.02772 [hep-th]. https://doi.org/10.1134/s0021364018220010
K. Aleshkin, A. Belavin, and A. Litvinov, J. Stat. Mech.: Theory Exp. 2019, 034003 (2019); arXiv: 1812.00478 [hep-th]. https://doi.org/10.1088/1742-5468/ab081a
A. A. Belavin and B. A. Eremin, Theor. Math. Phys. 201, 1606 (2019); arXiv: 1907.11102 [hep-th]. https://doi.org/10.1134/s0040577919110060
K. Aleshkin and A. Belavin, J. Phys. A 51, 055403 (2018); arXiv: 1706.05342[hep-th]. https://doi.org/10.1088/1751-8121/aa9e7a
H. Jockers, V. Kumar, J. M. Lapan, D. R. Morrison, and M. Romo, Commun. Math. Phys. 325, 1139 (2014); arXiv: 1208.6244. https://doi.org/10.1007/s00220-013-1874-z
Acknowledgments
We are grateful to A. Belavin and M. Belakovskii for the stimulating discussions.
Author information
Authors and Affiliations
Corresponding authors
Additional information
Russian Text © The Author(s), 2020, published in Pis’ma v Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2020, Vol. 112, No. 5, pp. 291–296.
Funding
This work was supported by the Russian Science Foundation (project no. 18-12-00439)
Rights and permissions
About this article
Cite this article
Artem’ev, A.A., Kochergin, I.V. On the Calculation of the Special Geometry for a Calabi—Yau Loop Manifold and Two Constructions of the Mirror Manifold. Jetp Lett. 112, 263–268 (2020). https://doi.org/10.1134/S0021364020170051
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0021364020170051