The Exact MSSM Spectrum from String Theory

TL;DR

This paper demonstrates the construction of string theory vacua that precisely reproduce the matter content of the MSSM, including three families, right-handed neutrinos, and no exotic matter, via heterotic string compactification.

Contribution

It provides an explicit example of a heterotic string compactification yielding the exact MSSM spectrum with realistic gauge groups and matter content, without extra vector-like pairs or exotic matter.

Findings

Realistic MSSM spectrum achieved from string theory

No extra vector-like pairs or exotic matter in the spectrum

Contains three families with right-handed neutrinos and one Higgs pair

Abstract

We show the existence of realistic vacua in string theory whose observable sector has exactly the matter content of the MSSM. This is achieved by compactifying the E_8 x E_8 heterotic superstring on a smooth Calabi-Yau threefold with an SU(4) gauge instanton and a Z_3 x Z_3 Wilson line. Specifically, the observable sector is N=1 supersymmetric with gauge group SU(3)_C x SU(2)_L x U(1)_Y x U(1)_{B-L}, three families of quarks and leptons, each family with a right-handed neutrino, and one Higgs-Higgs conjugate pair. Importantly, there are no extra vector-like pairs and no exotic matter in the zero mode spectrum. There are, in addition, 6 geometric moduli and 13 gauge instanton moduli in the observable sector. The holomorphic SU(4) vector bundle of the observable sector is slope-stable.