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String derived MSSM and M-theory unification. (English) Zbl 1016.81506

Summary: The recent conjecture of possible equivalence between the string scale \(M_S\) and the minimal supersymmetric standard model unification scale \(M_U\approx 2.5\times 10^{16}\) GeV is considered in the context of string models. This conjecture suggests that the observable gauge group just below the string scale should be \(SU(3)_C\times\text{SU}(2)_L\times\text{U}(1)_Y\) and that the \(SU(3)_C\times\text{SU}(2)_L\times\text{U}(1)_Y\)-charged spectrum of the observable sector should consist solely of the MSSM spectrum. We demonstrate that string models can actually be constructed that possess these observable features. Two aspects generic to many classes of three family \(SU(3)_C\times\text{SU}(2)_L\times\text{U}(1)_Y\) string models are both an extra local anomalous \(U(1)_A\) and numerous (often fractionally charged) exotic particles beyond the MSSM. Thus, for these classes, the key to obtaining an \(M_S=M_U\approx 2.5\times 10^{16}\) GeV string model is the existence of F- and D-flat directions that near the string scale can simultaneously break the anomalous \(U(1)\) and give mass to all exotic SM-charged observable particles, decoupling them from the low energy spectrum. In this letter we show, in the context of free fermionic strings, that string models with flat directions possessing these features do exist. We present one such string derived model in which all such exotic observable states beyond the MSSM receive mass at the scale generated by the Fayet-Iliopoulos term. The associated F- and D-flat direction is proven flat to all orders of the superpotential.

MSC:

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