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Moduli dependent \(\mu \)-terms in a heterotic standard model. (English) Zbl 1226.81169
Summary: In this paper, we present a formalism for computing the non-vanishing Higgs \(\mu \)-terms in a heterotic standard model. This is accomplished by calculating the cubic product of the cohomology groups associated with the vector bundle moduli (\(\phi\)), Higgs \((H)\) and Higgs conjugate (\(\overline{H}\)) superfields. This leads to terms proportional to \(\phi H\overline{H}\) in the low energy superpotential which, for non-zero moduli expectation values, generate moduli dependent \(\mu \)-terms of the form \(\langle \phi\rangle H\overline{H}\). It is found that these interactions are subject to two very restrictive selection rules, each arising from a Leray spectral sequence, which greatly reduce the number of moduli that can couple to Higgs-Higgs conjugate fields. We apply our formalism to a specific heterotic standard model vacuum. The non-vanishing cubic interactions \(\phi H\overline{H}\) are explicitly computed in this context and shown to contain only four of the nineteen vector bundle moduli.

MSC:
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81V22 Unified quantum theories
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