Superconformal algebras for generalized Spin(7) and G${}_2$ connected sums

Abstract

Worldsheet string theory compactified on exceptional holomony manifolds is revisited following arXiv:1809.06376, where aspects of the chiral symmetry were described for the case where the compact space is a 7-dimensional G${}_2$-holonomy manifold constructed as a Twisted Connected Sum. We reinterpret this result and extend it to Extra Twisted Connected Sum G${}_2$-manifolds, and to 8-dimensional Generalized Connected Sum Spin(7)-manifolds. Automorphisms of the latter construction lead us to conjecture new mirror maps.

arXiv commentReference added, minor changes in sections 3 and 4 to match published version. 34 pages

References in corpus (47)

• Compactification of D=11 supergravity on spaces of exceptional holonomy
• Chiral de Rham complex
• 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
• On Mirror Symmetry for Manifolds of Exceptional Holonomy
• A note on the extended superconformal algebras associated with manifolds of exceptional holonomy
• Rolling among G_2 vacua
• 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
• On TCS $G_2$ manifolds and 4D Emergent Strings
• Rational Conformal Field Theories With G_2 Holonomy
• Generalised discrete torsion and mirror symmetry for G_2 manifolds
• On Gauge Enhancement and Singular Limits in $G_2$ Compactifications of M-theory
• Infinitely Many M2-instanton Corrections to M-theory on $G_2$-manifolds
• CFT Description of String Theory Compactified on Non-compact Manifolds with G_2 Holonomy
• String Theory on G_2 Manifolds Based on Gepner Construction
• An Algorithmic Approach to Operator Product Expansions, $W$-Algebras and $W$-Strings
• Cascade of Special Holonomy Manifolds and Heterotic String Theory
• Unitary minimal models of SW(3/2,3/2,2) superconformal algebra and manifolds of G_2 holonomy
• Tops as Building Blocks for G2 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
• Open G2 Strings
• 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
• Superconformal Field Theories for Compact Manifolds with Spin(7) Holonomy
• Unitary representations of SW(3/2,2) superconformal algebra
• Coset Construction of Noncompact Spin(7) and G_2 CFTs
• Deformations of asymptotically cylindrical G_2 manifolds
• Supercoset CFT's for String Theories on Non-compact Special Holonomy Manifolds
• Superconformal algebras for twisted connected sums and $G_2$ mirror symmetry
• Asymptotically cylindrical 7-manifolds of holonomy G_2 with applications to compact irreducible G_2-manifolds
• Exceptional Algebra and Sporadic Groups at c=12
• Geometric Unification of Higgs Bundle Vacua
• $\mathcal{G}$-structure symmetries and anomalies in $(1,0)$ non-linear $\sigma$-models
• On Mirror Maps for Manifolds of Exceptional Holonomy
• Local $G_2$-Manifolds, Higgs Bundles and a Colored Quantum Mechanics
• A Note on Mirror Symmetry for Manifolds with Spin(7) Holonomy
• Mirror symmetry aspects for compact G_2 manifolds
• G-structures and Superstrings from the Worldsheet
• Noncritical strings and W-algebras
• Nu-invariants of extra-twisted connected sums

Cited by in corpus (3)

• Topological G${}_2$ and Spin(7) strings at 1-loop from double complexes
• $\mathcal{S}\mathcal{W}$-algebras and strings with torsion
• Families of solutions of the heterotic G${}_2$ system