Abstract
The heterotic--string models in the free fermionic formulation gave rise to some of the most realistic string models to date, which possess N=1 spacetime supersymmetry. Lack of evidence for supersymmetry at the LHC instigated recent interest in non-supersymmetric heterotic-string vacua. We explore what may be learned in this context from the quasi--realistic free fermionic models. We show that constructions with a low number of families give rise to proliferation of a priori tachyon producing sectors, compared to the non--realistic examples, which typically may contain only one such sector. The reason being that in the realistic cases the internal six dimensional space is fragmented into smaller units. We present one example of a quasi--realistic, non--supersymmetric, non--tachyonic, heterotic--string vacuum and compare the structure of its massless spectrum to the corresponding supersymmetric vacuum. While in some sectors supersymmetry is broken explicitly, i.e. the bosonic and fermionic sectors produce massless and massive states, other sectors, and in particular those leading to the chiral families, continue to exhibit fermi-bose degeneracy. In these sectors the massless spectrum, as compared to the supersymmetric cases, will only differ in some local or global U(1) charges. We discuss the conditions for obtaining $n_b=n_f$ at the massless level in these models. Our example model contains an anomalous U(1) symmetry, which generates a tadpole diagram at one loop-order in string perturbation theory. We speculate that this tadpole diagram may cancel the corresponding diagram generated by the one-loop non-vanishing vacuum energy and that in this respect the supersymmetric and non-supersymmetric vacua should be regarded on equal footing. Finally we discuss vacua that contain two supersymmetry generating sectors.
Highlights
The discovery of the agent of electroweak symmetry breaking at the LHC [1,2] is a pivotal moment in particle physics
The observation of a scalar resonance compatible with the electroweak Higgs doublet reinforces the hypothesis that the Standard Model provides a viable parameterisation of all sub-atomic data up to the Planck scale
Synthesis of gravity with the sub-atomic interactions necessitates a departure from the local point particle idealisation of quantum field theories, which underly the Standard Model
Summary
The discovery of the agent of electroweak symmetry breaking at the LHC [1,2] is a pivotal moment in particle physics. It should be stressed that these free fermionic models correspond to Z2 × Z2 toroidal orbifolds and their phenomenological characteristics are deeply rooted in the structure of the Z2 × Z2 orbifolds In this respect, the free fermionic formalism merely provides an accessible set of tools to extract the spectra of the string vacua and their properties. The 18 left-moving worldsheet fermions χ I transform in the adjoint representation of the Lie group, which in the case of the fermionic Z2 × Z2 orbifolds with N = 1 SUSY is SU (2). The 18 left-moving worldsheet fermions χ I transform in the adjoint representation of the Lie group, which in the case of the fermionic Z2 × Z2 orbifolds with N = 1 SUSY is SU (2)6 Such models provide our starting point and we will discuss in later sections how supersymmetry is broken. Further details on the formalism and notation used in the free fermionic construction can be found in the literature [9,10,11,12,13,14,15,16,17,18,19,43,44,45,46,47,48,49,50]
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