Multiple mirrors and the JKLMR conjecture
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 CalabiYau manifolds. The problem is considered for a specific class of CalabiYau manifolds that does not belong to the Fermat type class. We show that the JKLMR conjecture holds when a CalabiYau manifold $X(1)$ of such type has a mirror partner $Y(1)$ in a weighted projective space that also admits a CalabiYau 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 $X(1)$.
 Publication:

Theoretical and Mathematical Physics
 Pub Date:
 October 2022
 DOI:
 10.1134/S0040577922100105
 Bibcode:
 2022TMP...213.1441B
 Keywords:

 CalabiYau manifold;
 mirror symmetry;
 multiple mirrors;
 CalabiYau moduli space