Abstract
Recently, at least 50 million of novel examples of compact G2 holonomy manifolds have been constructed as twisted connected sums of asymptotically cylindrical Calabi-Yau threefolds. The purpose of this paper is to study mirror symmetry for compactifications of Type II superstrings in this context. We focus on G2 manifolds obtained from building blocks constructed from dual pairs of tops, which are the closest to toric CY hypersurfaces, and formulate the analogue of the Batyrev mirror map for this class of G2 holonomy manifolds, thus obtaining several millions of novel dual superstring backgrounds. In particular, this leads us to conjecture a plethora of novel exact dualities among the corresponding 2d mathcal{N} = 1 sigma models.
Highlights
Going to be the focus of the present note, arises from four T-dualities via a generalization of the SYZ argument [13]
We focus on G2 manifolds obtained from building blocks constructed from dual pairs of tops, which are the closest to toric CY hypersurfaces, and formulate the analogue of the Batyrev mirror map for this class of G2 holonomy manifolds, obtaining several millions of novel dual superstring backgrounds
Similar conjectures were originally formulated in the context of appropriate 2d extended N = 1 SCFTs describing strings propagating on G2-holonomy manifolds [10]
Summary
Let us begin with a quick informal review of the construction of TCS G2holonomy manifolds [24, 25, 46]. Consider the mirrors X±∨ of the asymptotically cylindrical Calabi-Yau manifolds X± and let L± be the corresponding SYZ special lagrangian T 3 [8]. Notice that in the asymptotically cylindrical region where the twisted connected sum occurs, we see that two of the four T-dualities occur along the Λ± special lagrangians within the smooth asymptotic K3 surfaces S±, inducing mirror symmetries on the asymptotic K3 fibres in the glueing region. G∨ : S+◦ → S−◦ is a hyperkahler rotation, as desired This concludes our heuristic argument showing that J∨ is a G2-holonomy manifold obtained as a twisted connected sum of the pair (X+∨, X−∨), which are the CY mirrors of (X+, X−). Calabi-Yau threefolds constructed from dual tops [30]
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