Can string theory predict the Weinberg angle?

Abstract

We investigate whether the hypercharge assignments in the standard model can be interpreted as a hint at grand unification in the context of heterotic string theory. Our analysis is a follow-up to the recent minilandscape analysis of the Z 6 -II orbifold of the E 8 E 0 8 heterotic string. In that analysis, an intermediate grand unified theory (GUT) was a requirement for finding MSSM-like theories. Nevertheless, about 1% of the models in this mini-landscape were MSSM-like. In this paper we remove this GUT restriction. To this end, we introduce a general method to calculate U1 Y for any heterotic orbifold and compare our findings to the cases where hypercharge arises from a GUT. Surprisingly, in the overwhelming majority of 3-2 standard models, a nonanomalous hypercharge direction can be defined, for which the spectrum is vectorlike. For these models, we calculate sin 2 w to see how well it agrees with the standard GUT value. We find that 12% have sin 2 w 3=8, while all others have values which are less. Finally, 89% of the models with sin 2 w 3=8 have U1 Y SU5.

Heterotic ℤ6–IIMSSM orbifolds in blowup

“…Alternatively, one could think about models where the hypercharge is not arising from a GUT breaking like SU(5)→ SU(3)×SU(2)×U (1), but it includes a mixing with other U(1)'s present in heterotic models. Such a non-GUT embedding of the hypercharge in the heterotic orbifold has been considered in [72]. However, for the only model described explicitly there, the hypercharge is not perpendicular to all the bundle vectors that arise from the chosen gauge shift and Wilson lines, hence still the hypercharge is broken in complete blowup in that particular model.…”

A Simple Introduction to Gröbner Basis Methods in String Phenomenology

“…There is currently a great deal of interest in applying the methods of computational algebraic geometry to string phenomenology and closely related sub-fields of theoretical physics. For some examples of recent work see [1,2,3,4,5,6,7,8,9,10,11,12,13,14] and references therein. These papers utilise advances in algorithmic techniques in commutative algebra to study a wide range of subjects including various aspects of globally supersymmetric gauge theory [1,2,3,4,5,6], finding flux vacua in string phenomenology [7,8,9], studying heterotic model building on smooth Calabi-Yau in non-standard embeddings [10] and more besides [11,12,13,14].…”