The exact MSSM spectrum from string theory

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 × E 8 heterotic superstring on a smooth Calabi-Yau threefold with an SU(4) gauge instanton and a Z 3 × Z 3 Wilson line. Specifically, the observable sector is N = 1 supersymmetric with gauge groupthree 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.

Monad bundles in heterotic string compactifications

“…Despite substantial recent progress [12][13][14][15][16][17][18][19][20][21][22], heterotic model-building continues to present a number of formidable mathematical obstacles. In addition to a Calabi-Yau three-fold X, heterotic models require two holomorphic (poly-)stable vector bundles V andṼ .…”

Stable and metastable cosmic strings in heterotic M-theory

“…(2.15) and (2.16) that c 2 (X) is even for any r. One can check that c 2 (X) is also even for more complicated Calabi-Yau threefolds with a non-trivial homotopy group which were used in [14,15,16,17] for obtaining heterotic Standard Model vacua.…”

“…Such compactifications are very attractive from the phenomenological viewpoint. Recent results [14,15,16,17] show the possibility of obtaining the Standard Model spectrum with no extra exotic matter in this framework.…”

A Z2×Z2 standard model

“…Almost simultaneously, two constructions of models have been found that give rise to the exact (chiral) spectrum of the minimal supersymmetric extension of the standard model (SM), the MSSM. One of them is based on heterotic 6 -II orbifolds [6] and the other on smooth Calabi-Yau (CY) compactifications [7,8]. (See e.g.…”

“…It is unknown whether a complete blow-down of the potentially realistic smooth compactifications, obtained so far [7,8,21], to an exact (free orbifold) CFT description exists. On the other hand, many phenomenologically attractive orbifold models [10][11][12] cannot be completely blown up without destroying the phenomenological viability of these settings, as the hypercharge or another part of the standard model gauge group gets broken in the complete blow-up [19].…”