Mirror Symmetry for $G_2$-Manifolds: Twisted Connected Sums and Dual Tops

Abstract

Recently, at least 50 million of novel examples of compact $G_2$ 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 $G_2$ 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 $G_2$ 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 N=1 sigma models.

34 pages, comments welcome

References in corpus (7)

• Integral Cohomology and Mirror Symmetry for Calabi-Yau 3-folds
• The Landscape of M-theory Compactifications on Seven-Manifolds with $G_2$ Holonomy
• Origin of Abelian Gauge Symmetries in Heterotic/F-theory Duality
• On Gauge Enhancement and Singular Limits in $G_2$ Compactifications of M-theory
• Lattice polarized toric K3 surfaces
• Perturbative Derivation of Mirror Symmetry
• On the structure of supersymmetric T3 fibrations

Cited by in corpus (26)

• Black Hole Spin Constraints on the Mass Spectrum and Number of Axion-like Fields
• F-theory and Dark Energy
• No-scale and scale-separated flux vacua from IIA on G2 orientifolds
• Compact, Singular G2-Holonomy Manifolds and M/Heterotic/F-Theory Duality
• On TCS $G_2$ manifolds and 4D Emergent Strings
• Infinitely Many M2-instanton Corrections to M-theory on $G_2$-manifolds
• Higgs Bundles for M-theory on $G_2$-Manifolds
• T-Branes and $G_2$ Backgrounds
• Effective action from M-theory on twisted connected sum $G_2$-manifolds
• Spin(7)-Manifolds as Generalized Connected Sums and 3d N=1 Theories
• Towards Generalized Mirror Symmetry for Twisted Connected Sum $G_2$ Manifolds
• Eleven-Dimensional Supergravity in 4D, $N=1$ Superspace
• Superconformal algebras for twisted connected sums and $G_2$ mirror symmetry
• Marginal deformations of heterotic $G_2$ sigma models
• Emergent Strings in Type IIB Calabi--Yau Compactifications
• $\mathcal{G}$-structure symmetries and anomalies in $(1,0)$ non-linear $\sigma$-models
• Local $G_2$-Manifolds, Higgs Bundles and a Colored Quantum Mechanics
• On Mirror Maps for Manifolds of Exceptional Holonomy
• Mirror symmetry and elliptic Calabi-Yau manifolds
• Evidence for an Algebra of ${\mathbf{G}}_2$ Instantons
• A 5d perspective on the compactifications of 6d SCFTs to 4d $\mathcal{N}=1$ SCFTs
• Topological G${}_2$ and Spin(7) strings at 1-loop from double complexes
• Superconformal algebras for generalized Spin(7) and G${}_2$ connected sums
• Counting Associatives in Compact $G_2$ Orbifolds
• Quark and lepton mass matrices from localization in M-theory on $G_2$ orbifold
• G-structures and Superstrings from the Worldsheet