Three generations on the quintic quotient. (English) Zbl 1269.81109
Summary: A three-generation \(SU(5)\) GUT, that is \( 3 \times \left( {\mathbf{\underline{10}}} + {\mathbf{\underline{\bar{5}}}} \right) \) and a single \( {\mathbf{\underline{5}}} - {\mathbf{\underline {\bar{5}}}} \) pair, is constructed by compactification of the \(E _{8}\) heterotic string. The base manifold is the \( {\mathbb{Z}}_5 \times {\mathbb{Z}}_5 \)-quotient of the quintic, and the vector bundle is the quotient of a positive monad. The group action on the monad and its bundle-valued cohomology is discussed in detail, including topological restrictions on the existence of equivariant structures. This model and a single \( {\mathbb{Z}}_5 \) quotient are the complete list of three generation quotients of positive monads on the quintic.
MSC:
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 81T60 | Supersymmetric field theories in quantum mechanics |
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