Abstract
We address the problem of the fulfillment of the conjecture proposed by Jockers et al. (JKLMR conjecture) on the equality of the partition function of a supersymmetric gauged linear sigma model on the sphere \(S^2\) and the exponential of the Kähler potential on the moduli space of Calabi–Yau manifolds. The problem is considered for a specific class of Calabi–Yau manifolds that does not belong to the Fermat type class. We show that the JKLMR conjecture holds when a Calabi–Yau manifold \(X(1)\) of such type has a mirror partner \(Y(1)\) in a weighted projective space that also admits a Calabi–Yau manifold of Fermat type \(Y(2)\). Moreover, the mirror \(X(2)\) for \(Y(2)\) has the same special geometry on the moduli space of complex structures as the original \(X(1)\).
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Translated from Teoreticheskaya i Matematicheskaya Fizika, 2022, Vol. 213, pp. 149–162 https://doi.org/10.4213/tmf10341.
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Belavin, A.A., Eremin, B.A. Multiple mirrors and the JKLMR conjecture. Theor Math Phys 213, 1441–1452 (2022). https://doi.org/10.1134/S0040577922100105
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DOI: https://doi.org/10.1134/S0040577922100105