A Mirror Theorem for the Mirror Quintic
Y.-P. Lee, M. Shoemaker
TL;DR
This paper proves a mirror duality for the Fermat quintic threefold, showing that its B model corresponds to the A model of its mirror, thereby confirming mirror symmetry as a true duality.
Contribution
It establishes a mirror-dual statement that completes the symmetry between A and B models for the Fermat quintic threefold.
Findings
B model of Fermat quintic is equivalent to A model of its mirror
Confirms mirror symmetry as a true duality for the quintic threefold
Provides a rigorous mathematical proof of the mirror duality
Abstract
The celebrated Mirror Theorem states that the genus zero part of the A model (quantum cohomology, rational curves counting) of the Fermat quintic threefold is equivalent to the B model (complex deformation, variation of Hodge structure) of its mirror dual orbifold. In this article, we establish a mirror-dual statement. Namely, the B model of the Fermat quintic threefold is shown to be equivalent to the A model of its mirror, and hence establishes the mirror symmetry as a true duality.
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