Cascade of special holonomy manifolds and heterotic string theory Original Research Article

We investigate heterotic string theory on special holonomy manifolds including exceptional holonomy G2 and Spin(7) manifolds. The gauge symmetry is F4 in a G2 manifold compactification, and so(9) in a Spin(7) manifold compactification. We also study the cascade of the holonomies: so(8)⊃Spin(7)⊃G2⊃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 the modular invariant partition functions and analyze their massless spectra for G2 and Spin(7) orbifolds. We obtain the relation between topological numbers of the manifolds and multiplicities of matters in specific representations.