Constructing 5d orbifold grand unified theories from heterotic strings

Abstract

A three-generation Pati-Salam model is constructed by compactifying the heterotic string on a particular T^6/Z_6 Abelian symmetric orbifold with two discrete Wilson lines. The compactified space is taken to be the Lie algebra lattice G_2+SU(3)+SO(4). When one dimension of the SO(4) lattice is large compared to the string scale, this model reproduces many features of a 5d SO(10) grand unified theory compactified on an S^1/Z_2 orbifold. (Of course, with two large extra dimensions we can obtain a 6d SO(10) grand unified theory.) We identify the orbifold parities and other ingredients of the orbifold grand unified theories in the string model. Our construction provides a UV completion of orbifold grand unified theories, and gives new insights into both field theoretical and string theoretical constructions.

Figures (3)

• Figure 1: $G_2 \oplus SU(3) \oplus SO(4)$ lattice with $\mathbb Z_2$ fixed points. The $T_{3}$ twisted sector states sit at these fixed points. The fixed point at the origin and the symmetric linear combination of the red (grey) fixed points in the $G_2$ torus have $\gamma =1$.
• Figure 2: $G_2 \oplus SU(3) \oplus SO(4)$ lattice with $\mathbb Z_3$ fixed points. The fixed point at the origin and the symmetric linear combination of the red (grey) fixed points in the $G_2$ torus have $\gamma =1$. The fields $V, \ \Sigma, \ $ and $1\times({\bf 16} + {\bf\overline{16}})$ are bulk states from the untwisted sector. On the other hand, $6\times({\bf 10} + {\bf\overline{10}})$ and $3\times({\bf 16} + {\bf\overline{16}})$ are "bulk" states located on the $T_{2}/T_{4}$ twisted sector fixed points.
• Figure 3: $G_2 \oplus SU(3) \oplus SO(4)$ lattice with $\mathbb Z_6$ fixed points. The $T_{1}$ twisted sector states sit at these fixed points.