Finding the Mirror of the Beauville Manifold

Details Finding the Mirror of the Beauville Manifold Finding the Mirror of the Beauville Manifold

2003-12-05

arxiv.org/abs/hep-th/0312056v1

Physics

High Energy Physics

High Energy Physics - Theory

22pp, LaTeX2e, utarticle.cls, utphys.bst

Scientific paper

We construct the mirror of the Beauville manifold. The Beauville manifold is a Calabi-Yau manifold with non-abelian fundamental group. We use the conjecture of Batyrev and Borisov to find the previously misidentified mirror of its universal covering space, $\mathbb{P}^7[2,2,2,2]$. The monomial-divisor mirror map is essential in identifying how the fundamental group of the Beauville manifold acts on the mirror of $\mathbb{P}^7[2,2,2,2]$. Once we find the mirror of the Beauville manifold, we confirm the existence of the threshold bound state around the conifold point, which was originally conjectured in hep-th/0106262. We also consider how the quantum symmetry group acts on the D-branes that become massless at the conifold point and show the action proposed in hep-th/0102018 is compatible with mirror symmetry.

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