Superconformal algebras for twisted connected sums and $G_2$ mirror symmetry

Abstract

We realise the Shatashvili-Vafa superconformal algebra for $G_2$ string compactifications by combining Odake and free conformal algebras following closely the recent mathematical construction of twisted connected sum $G_2$ holonomy manifolds. By considering automorphisms of this realisation, we identify stringy analogues of two mirror maps proposed by Braun and Del Zotto for these manifolds.

arXiv comment29 pages

References in corpus (33)

• Mirror Symmetry is T-Duality
• W-symmetry in Conformal Field Theory
• On Orbifolds with Discrete Torsion
• Compactification of D=11 supergravity on spaces of exceptional holonomy
• Supersymmetric Cycles in Exceptional Holonomy Manifolds and Calabi-Yau 4-Folds
• G_2-manifolds and associative submanifolds via semi-Fano 3-folds
• Holonomy groups and W-symmetries
• Asymptotically cylindrical Calabi-Yau 3-folds from weak Fano 3-folds
• A note on the extended superconformal algebras associated with manifolds of exceptional holonomy
• On Mirror Symmetry for Manifolds of Exceptional Holonomy
• Superconformal Field Theories for Compact G_2 Manifolds
• Mirror Symmetry for $G_2$-Manifolds: Twisted Connected Sums and Dual Tops
• The Landscape of M-theory Compactifications on Seven-Manifolds with $G_2$ Holonomy
• Compact, Singular G2-Holonomy Manifolds and M/Heterotic/F-Theory Duality
• The ${\alpha }^{\prime }$ Expansion On A Compact Manifold Of Exceptional Holonomy
• Rational Conformal Field Theories With G_2 Holonomy
• On Gauge Enhancement and Singular Limits in $G_2$ Compactifications of M-theory
• Generalised discrete torsion and mirror symmetry for G_2 manifolds
• Infinitely Many M2-instanton Corrections to M-theory on $G_2$-manifolds
• String Theory on G_2 Manifolds Based on Gepner Construction
• Cascade of Special Holonomy Manifolds and Heterotic String Theory
• Tops as Building Blocks for G2 Manifolds
• Unitary minimal models of SW(3/2,3/2,2) superconformal algebra and manifolds of G_2 holonomy
• Effective action from M-theory on twisted connected sum $G_2$-manifolds
• Moduli spaces of G2 manifolds
• Dirichlet Joyce Manifolds, Discrete Torsion and Duality
• Spin(7)-Manifolds as Generalized Connected Sums and 3d N=1 Theories
• Towards Generalized Mirror Symmetry for Twisted Connected Sum $G_2$ Manifolds
• Supercoset CFT's for String Theories on Non-compact Special Holonomy Manifolds
• Coset Construction of Noncompact Spin(7) and G_2 CFTs
• New N=1 Extended Superconformal Algebras with Two and Three Generators
• Spacetime supersymmetry in low-dimensional perturbative heterotic compactifications
• Marginal deformations of heterotic $G_2$ sigma models

Cited by in corpus (10)

• Higgs Bundles for M-theory on $G_2$-Manifolds
• T-Branes and $G_2$ Backgrounds
• $\mathcal{G}$-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
• A 5d perspective on the compactifications of 6d SCFTs to 4d $\mathcal{N}=1$ SCFTs
• Superconformal algebras for generalized Spin(7) and G${}_2$ connected sums
• SW(3/2,2) subsymmetry in G${}_2$, Spin(7) and N=2 CFTs
• Mink${}_4\times S^2$ Solutions of 10 and 11 Dimensional Supergravity
• $\mathcal{S}\mathcal{W}$-algebras and strings with torsion