Chiral family classification of fermionic Z2×Z2 heterotic orbifold models

Free fermionic construction of four-dimensional string vacua, are related to the Z2×Z2 orbifolds at special points in the moduli space, and yielded the most realistic three family string models to date. Using free fermionic construction techniques we are able to classify more than 1010 string vacua by the net family and anti-family number. Using a Monte Carlo technique we find a bell shaped distribution that peaks at vanishing net number of chiral families. We also observe that ∼15% of the models have three net chiral families. In addition to mirror symmetry we find that the distribution exhibits a symmetry under the exchange of (spinor plus anti-spinor) representations with vectorial representations.