This article is cited in 1 paper

Multiple mirrors and the JKLMR conjecture

A. A. Belavin^ab, B. A. Eremin<sup>bcd

a</sup> Landau Institute for Theoretical Physics of Russian Academy of Sciences, Chernogolovka, Russia
^b Kharkevich Institute for Information Transmission Problems, Moscow, Russia
^c Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Region, Russia
^d Skolkovo Institute of Science and Technology, Moscow, Russia

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 $X(1)$.

Keywords: Calabi–Yau manifold, mirror symmetry, multiple mirrors, Calabi–Yau moduli space.

Received: 29.07.2022
Revised: 29.07.2022

DOI: 10.4213/tmf10341

 English version: Theoretical and Mathematical Physics, 2022, 213:1, 1441–1452

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