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3 papers
METHODS OF THEORETICAL PHYSICS
Mirror pairs of quintic orbifolds
A. A. Belavinabc,
B. A. Eremindcba a Landau Institute for Theoretical Physics, Russian Academy of Sciences,
Chernogolovka, Moscow region, 142432 Russia
b Institute for Information Transmission Problems (Kharkevich Institute),
Russian Academy of Sciences, Moscow, 127994 Russia
c Moscow Institute of Physics and Technology (National Research University),
Dolgoprudnyi, Moscow region, 141700 Russia
d Skolkovo Institute of Science and Technology (Skoltech),
Skolkovo, Moscow region, 143025 Russia
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
$W_Y$ is determined from the properties of the polynomial
$W_X$ specifying the Calabi-Yau manifold
$X$. The polynomial
$W_Y$ is determined in an explicit form. The group of symmetry of the polynomial
$W_Y$ is found from its form and it is tested whether it coincides with that predicted by the Berglund–Hubsch–Krawitz construction.
Received: 03.09.2020
Revised: 03.09.2020
Accepted: 03.09.2020
DOI:
10.31857/S1234567820180111
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