Abstract
The strongly coupled heterotic M-theory vacuum for both the observable and hidden sectors of the B − L MSSM theory is reviewed, including a discussion of the “bundle” constraints that both the observable sector SU(4) vector bundle and the hidden sector bundle induced from a single line bundle must satisfy. Gaugino condensation is then introduced within this context, and the hidden sector bundles that exhibit gaugino condensation are presented. The condensation scale is computed, singling out one line bundle whose associated condensation scale is low enough to be compatible with the energy scales available at the LHC. The corresponding region of Kähler moduli space where all bundle constraints are satisfied is presented. The generic form of the moduli dependent F-terms due to a gaugino superpotential — which spontaneously break N = 1 supersymmetry in this sector — is presented and then given explicitly for the unique line bundle associated with the low condensation scale. The moduli-dependent coefficients for each of the gaugino and scalar field soft supersymmetry breaking terms are computed leading to a low-energy effective Lagrangian for the observable sector matter fields. We then show that at a large number of points in Kähler moduli space that satisfy all “bundle” constraints, these coefficients are initial conditions for the renormalization group equations which, at low energy, lead to completely realistic physics satisfying all phenomenological constraints. Finally, we show that a substantial number of these initial points also satisfy a final constraint arising from the quadratic Higgs-Higgs conjugate soft supersymmetry breaking term.
Highlights
E8 group is broken to the SU(3)C × SU(2)L × U(1)Y standard model gauge group with an additional U(1)B−L gauge group factor
We will show that a substantial subset of these initial conditions — referred to as “red” points — satisfy a new constraint imposed on the coefficient of the Higgs-Higgs conjugate soft supersymmetry breaking term
We present the generic properties a line bundle L must possess to be equivariant on our specific Schoen Calabi-Yau, the explicit embedding of its U(1) structure group into the SU(2) factor of SU(2) × E7 ⊂ E8 via the “induced” Whitney sum bundle L ⊕ L−1, and the constraint imposed on L so that this induced vector bundle is poly-stable
Summary
On the observable orbifold plane, the vector bundle is chosen to be a specific holomorphic bundle with structure group SU(4) ⊂ E8 [22]. Spin(10) is the “grand unified” group of the observable sector This GUT group is further broken at the scale MU = 3.15 × 1016 GeV to the low energy gauge group of the B − L MSSM by turning on two flat Wilson lines, each associated with a different Z3 factor of the Z3 × Z3 symmetry of X. Doing this preserves the N = 1 supersymmetry of the four-dimensional effective theory, but breaks the observable sector gauge group down to. We will show in the following that the physically realistic region of Kähler moduli space is further constrained by the gauge bundle in the hidden sector
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