Abstract
Some of the supersymmetric nonlinear sigma models on exceptional groups (E7 or E8) are known to yield almost minimal necessary content of matter fields for phenomenological model building, including three chiral families and a Higgs multiplet. We explore a possible realization of such a family unification in heterotic string theory, where the spontaneously broken symmetry that we focus on is the one associated with the change of global orientation of the spin bundle embedded in the gauge bundle, which cannot be ignored in the presence of a magnetic source of the B field. We show in a simple model that it indeed gives rise to chiral matter fields on the defect similarly to the domain-wall fermions, and compare the chiral zero mode spectrum with the sigma model. The setup is reduced to a system similar to that postulated in the orbifold GUT or the grand gauge-Higgs unification model, where the origin of Z2 identification is accounted for as arising from the bolt of the Atiyah-Hitchin manifold.
Highlights
Some of the supersymmetric nonlinear sigma models on exceptional groups (E7 or E8) are known to yield almost minimal necessary content of matter fields for phenomenological model building, including three chiral families and a Higgs multiplet
One of the major obstacles in constructing realistic phenomenological models in string theory is the appearance of numerous moduli, which are ever present in any smooth supersymmetric compactifications
They are problematic for phenomenological applications of string theory for the following reasons: First, they may cause the cosmological moduli problem [1]. If they are present to date, their masses must be light enough in order for their energy density not to exceed the observed cosmological bound. If they are assumed to have decayed, there is a risk that they may spoil the success of the BBN scenario or the released entropy may dilute the baryon asymmetry produced by that time, depending on the time they decay
Summary
In field theory (as opposed to string theory), an interesting proposal had been put forward in [15] long time ago, even before superstring theories have come to be known, where it was suggested that the quarks and leptons could be understood as quasi-Nambu-Goldstone fermions [16] of a supersymmetric nonlinear sigma model [15, 17,18,19,20, 22]. For the purpose of obtaining more realistic cosets, we perform a similar computation in the background with a constant U(1) Wilson line in addition to the SU(3) gauge configuration This time, a pair of chiral and anti-chiral modes turn out to appear and are asymmetrically localized on different branes, being unsatisfactory as a realization of the E8/(SO(10) × H) coset. Some useful facts about E8 and conventions for the gamma matrices are collected in two appendices
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