Cascade of Special Holonomy Manifolds and Heterotic String Theory

Abstract

We investigate hetrotic string theory on special holonomy manifolds including exceptional holonomy G_2 and Spin(7) manifolds. The gauge symmetry is F_4 in a G_2 manifold compactification, and so(9) in a Spin(7) manifold compactification. We also study the cascade of the holonomies: so(8) > Spin(7) > G_2 > su(3) > su(2). The differences of adjoining groups are described by Ising, tricritical Ising, 3-state Potts and u(1) models. These theories are essential for spacetime supersymmetries and gauge group enhancements. As concrete examples, we construct modular invariant partition functions and analyze their massless spectra for G_2 and Spin(7) orbifolds. We obtain the relation between topological numbers of the manifolds and multiplicities of matters in specific representations.

49 pages, LaTeX, no figure, minor changes, typos corrected, references added

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• Superconformal Field Theories for Compact G_2 Manifolds
• Rational Conformal Field Theories With G_2 Holonomy
• Supersymmetry, G-flux and Spin(7) manifolds
• Unitary minimal models of SW(3/2,3/2,2) superconformal algebra and manifolds of G_2 holonomy
• D-brane probes on G2 Orbifolds
• Supercoset CFT's for String Theories on Non-compact Special Holonomy Manifolds
• Coset Construction of Noncompact Spin(7) and G_2 CFTs
• Superconformal algebras for twisted connected sums and $G_2$ mirror symmetry
• Heterotic strings on G_2 orbifolds
• Type IIA Orientifold Limit of M-Theory on Compact Joyce 8-Manifold of Spin(7)-Holonomy
• Comments on M Theory Dynamics on G2 Holonomy Manifolds
• Coset Character Identities in Superstring Compactifications
• Superconformal algebras for generalized Spin(7) and G${}_2$ connected sums
• $\mathcal{S}\mathcal{W}$-algebras and strings with torsion
• Discrete Torsion in Singular G_2-Manifolds and Real LG
• Bootstrapping Boundaries and Branes