Heterotic mini-landscape (II): completing the search for MSSM vacua in a Z_6 orbifold

TL;DR

Problem: finding exact MSSM vacua in string theory is extremely difficult; this work extends the search to the Z6-II heterotic orbifold with 3 Wilson lines. Approach: combine a local-GUT–driven strategy with a statistical sampling method to estimate the total model count (~10^7) and to enumerate MSSM candidates; present explicit 3-WL models and an illustrative example. Key findings: nearly 300 inequivalent MSSM vacua satisfy spectrum, gauge coupling unification, and a heavy top; most arise from SO(10), E6, or SU(5) local GUTs; the hidden-sector gauge content biases gaugino condensation scales toward TeV-scale soft masses. Significance: supports a top-down rationale for TeV-scale SUSY and clarifies how local GUT structure shapes the MSSM landscape in a richly degenerate string vacuum space.

Abstract

We complete our search for MSSM vacua in the Z_6-II heterotic orbifold by including models with 3 Wilson lines. We estimate the total number of inequivalent models in this orbifold to be 10^7. Out of these, we find almost 300 models with the exact MSSM spectrum, gauge coupling unification and a heavy top quark. Models with these features originate predominantly from local GUTs. The scale of gaugino condensation in the hidden sector is correlated with properties of the observable sector such that soft masses in the TeV range are preferred.

Figures (2)

• Figure 1: Number of MSSM candidates vs. largest gauge group in the hidden sector. $\mathrm{SU}(N)$/$\mathrm{SO}(2N)$/$\mathrm{E}_{N}$ are given by light/dark/darker bins. (a): models with 3 WL, (b): models with 2 and 3 WL.
• Figure 2: Number of MSSM candidates with 2 and 3 Wilson lines vs. the scale of gaugino condensation.