Discrete Symmetry and GUT Breaking

TL;DR

This paper explores how discrete symmetries in extra dimensions can break supersymmetric GUT models down to the Standard Model, offering new mechanisms for GUT symmetry breaking and KK state mass hierarchies.

Contribution

It introduces novel methods of GUT breaking via discrete symmetries in various extra-dimensional geometries, including brane neighborhoods and specific manifolds like annulus and disc.

Findings

Discrete symmetries can break GUT gauge symmetry in extra dimensions.

Models allow for large extra dimensions with heavy KK states.

Certain geometries yield only a few light KK states.

Abstract

We study the supersymmetric GUT models where the supersymmetry and GUT gauge symmetry can be broken by the discrete symmetry. First, with the ansatz that there exist discrete symmetries in the branes' neighborhoods, we discuss the general reflection $Z_2$ symmetries and GUT breaking on $M^4\times M^1$ and $M^4\times M^1\times M^1$. In those models, the extra dimensions can be large and the KK states can be set arbitrarily heavy. Second, considering the extra space manifold is the annulus $A^2$ or disc $D^2$, we can define any $Z_n$ symmetry and break any 6-dimensional N=2 supersymmetric SU(M) models down to the 4-dimensional N=1 supersymmetric $SU(3)\times SU(2)\times U(1)^{M-4}$ models for the zero modes. In particular, there might exist the interesting scenario on $M^4\times A^2$ where just a few KK states are light, while the others are relatively heavy. Third, we discuss the complete global discrete symmetries on $M^4\times T^2$ and study the GUT breaking.