## 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)

### Software:

STRINGVACUA; SINGULAR; Macaulay2
Full Text:

### References:

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