String derived MSSM and M-theory Unification

TL;DR

This work tackles the problem of reconciling the MSSM unification scale with string-scale physics by constructing a concrete free-fermionic string vacuum (the FNY model) in which the observable sector below the string scale is exactly the MSSM. By identifying F- and D-flat directions that cancel the anomalous $U_A$ Fayet-Iliopoulos term, the authors achieve decoupling of all SM-charged exotics and lift them near the FI/string scale, aligning the running of gauge couplings with the MSSM prediction at $M_U ≈ 2.5×10^{16}$ GeV. A key result is that the massless spectrum below the string scale reduces to the MSSM content, with a single light Higgs pair and exotics effectively decoupled, supporting the scenario in which $M_S$ may coincide with $M_U$. The analysis also shows how the flat direction necessarily breaks the anomalous and a related $U(1)_{Z'}$, leaving the SM gauge group $SU(3)_C×SU(2)_L×U(1)_Y$, which has important implications for string-based unification in the M-theory context. Overall, the paper provides a concrete, anomaly-consistent string vacuum achieving MSSM below the string scale and offers a pathway toward fully string-derived unification scenarios.

Abstract

The recent conjecture of possible equivalence between the string scale $M_S$ and the minimal supersymmetric standard model unification scale M_U ~ 2.5 x 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 x SU(2)_L x U(1)_Y and that the SU(3)_C x SU(2)_L x 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 x SU(2)_L x 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 ~ 2.5 x 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.