Multiple mirrors and the JKLMR conjecture. (English. Russian original) Zbl 1516.81164
Theor. Math. Phys. 213, No. 1, 1441-1452 (2022); translation from Teor. Mat. Fiz. 213, No. 1, 149-162 (2022).
Summary: We address the problem of the fulfillment of the conjecture proposed by H. Jockers et al. [Commun. Math. Phys. 325, No. 3, 1139–1170 (2014; Zbl 1301.81253)]
(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 \(X(1)\).
MSC:
81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
81T60 | Supersymmetric field theories in quantum mechanics |
14J32 | Calabi-Yau manifolds (algebro-geometric aspects) |
81T15 | Perturbative methods of renormalization applied to problems in quantum field theory |
81T16 | Nonperturbative methods of renormalization applied to problems in quantum field theory |
14D21 | Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) |
32Q15 | Kähler manifolds |
14N35 | Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) |
14J33 | Mirror symmetry (algebro-geometric aspects) |
81T13 | Yang-Mills and other gauge theories in quantum field theory |
32Q25 | Calabi-Yau theory (complex-analytic aspects) |
Citations:
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