Mirror symmetry aspects for compact G_2 manifolds

Abstract

The present paper deals with mirror symmetry aspects of compact ``barely'' $G_2$ manifolds, that is, $G_2$ manifolds of the form (CY$\times S^1)/{\mathbb{Z}}_2$. We propose that the mirror of any barely $G_2$ manifold is another barely one and which is constructed as a fibration of the \emph{mirror} of the CY base. Also, we describe the Joyce manifolds of the first kind as ``barely'' and we show that the underlying CY of all the family is self-mirror with $h^{1,1}=h^{2,1}=19$. We thus propose that the mirror of a Joyce space of the first kind will be another Joyce space of the first kind.We also suggest that this self-mirror CY family is dual to K3$\times S^1$ in the heterotic/M-theory sense, and that arise as a particular case of the Borcea-Voisin construction. As a spin-off we conclude from this analysis that no 5-brane instantons are present in compactifications of eleven dimensional supergravity over Joyce manifolds of the first kind.

19 pages, Latex, some explanation clarified

References in corpus (9)

• Fivebranes, Membranes and Non-Perturbative String Theory
• On Mirror Symmetry for Manifolds of Exceptional Holonomy
• Rolling among G_2 vacua
• N=1 Heterotic/M-theory Duality and Joyce Manifolds
• Open G2 Strings
• The Topological G2 String
• On the Global Structure of Some Natural Fibrations of Joyce Manifolds
• Towards A Topological G_2 String
• Mirror Duality in a Joyce Manifold

Cited by in corpus (3)

• Manifolds with parallel differential forms and Kaehler identities for G_2-manifolds
• Superconformal algebras for generalized Spin(7) and G${}_2$ connected sums
• Mirror Duality in a Joyce Manifold