Moduli Dependent mu-Terms in a Heterotic Standard Model

TL;DR

This paper develops a formalism to compute moduli-dependent mu-terms in heterotic string models by analyzing cubic cohomology products, revealing restrictive selection rules that limit moduli coupling to Higgs fields.

Contribution

It introduces a method to calculate moduli-dependent mu-terms in heterotic models and identifies key selection rules reducing possible couplings.

Findings

Only four of nineteen moduli couple to Higgs fields in the specific model.

The formalism explicitly computes cubic interactions involving moduli and Higgs fields.

Selection rules from Leray spectral sequences significantly restrict moduli-Higgs couplings.

Abstract

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 (Hbar) superfields. This leads to terms proportional to phi H Hbar in the low energy superpotential which, for non-zero moduli expectation values, generate moduli dependent mu-terms of the form <phi> H Hbar. 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 Hbar are explicitly computed in this context and shown to contain only four of the nineteen vector bundle moduli.