N=2 6-dimensional Supersymmetric $E_6$ Breaking

TL;DR

This paper explores how to break supersymmetry and gauge symmetry in 6D $E_6$ models via discrete symmetries, resulting in 4D models with realistic gauge groups and Higgs content, including constraints and specific models.

Contribution

It introduces a method for symmetry breaking in 6D $E_6$ models using discrete symmetries, leading to realistic 4D supersymmetric models with detailed constraints and examples.

Findings

Derived 4D $N=1$ models with specific gauge groups from 6D $E_6$ models.

Listed constraints for constructing models on annulus and disc manifolds.

Presented a simple model with $Z_9$ symmetry.

Abstract

We study the $N=2$ supersymmetric $E_6$ models on the 6-dimensional space-time where the supersymmetry and gauge symmetry can be broken by the discrete symmetry. On the space-time $M^4\times S^1/(Z_2\times Z_2') \times S^1/(Z_2\times Z_2')$, for the zero modes, we obtain the 4-dimensional $N=1$ supersymmetric models with gauge groups $SU(3)\times SU(2) \times SU(2) \times U(1)^2$, $SU(4)\times SU(2) \times SU(2) \times U(1)$, and $SU(3)\times SU(2) \times U(1)^3$ with one extra pair of Higgs doublets from the vector multiplet. In addition, considering that the extra space manifold is the annulus $A^2$ and disc $D^2$, we list all the constraints on constructing the 4-dimensional $N=1$ supersymmetric $SU(3)\times SU(2) \times U(1)^3$ models for the zero modes, and give the simplest model with $Z_9$ symmetry. We also comment on the extra gauge symmetry breaking and its generalization.