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Yukawa couplings in heterotic compactification. (English) Zbl 1203.81130

Yukawa couplings – more precisely, their \(F\)-term contribution coming from the superpotential – play a prominent role in the characterization of phenomenologically viable models arising from superstring compactifications. An important task of string phenomenology is to provide an effective way of computing them for a given string background. In the heterotic context, most of the results were restricted to the case when the gauge bundle \(V\to X\) on the internal Calabi-Yau manifold \(X\) is its holomorphic tangent bundle.
This paper improves the situation by giving an effective, algorithmic way of computing Yukawas when \(V\) is a polystable holomorphic vector bundle constructed via the monad method, and \(X\) is a (favourable) Calabi-Yau complete intersection in \(\mathbb{P}^{n_1}\times \dots \times \mathbb{P}^{n_k}\). The power of the method stems from the fact, for these configurations, Cech cohomology groups of \(V\) can be presented as quotients of polynomial rings, and the computation of Yukawa couplings is reduced to the operation of multiplying polynomials and to a projection on a distinguished one-dimensional subspace. This results in a purely algebraic formalism, which the authors exploit in the case with no anti-generations and with GUT gauge group \(E_6\), \(SO(10)\) and \(SU(5)\). Some remarks on the relation of this method and the heterotic engineering of \(SO(10)\) one-Higgs models are also included.

MSC:

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
14J81 Relationships between surfaces, higher-dimensional varieties, and physics
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
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