Minimal String Model in $Z_4$, $Z_6$ and $Z_8$ Orbifold Constructions

TL;DR

This paper investigates the possibility of deriving the Minimal Supersymmetric Standard Model (MSSM) from specific orbifold string constructions, analyzing anomaly cancellation, gauge coupling thresholds, and experimental consistency.

Contribution

It identifies which $Z_N$ orbifold models can produce the MSSM spectrum and determines allowable levels of hypercharge normalization.

Findings

$Z_6$-I, $Z_6$-II, and $Z_8$-I orbifolds can produce the MSSM.

Allowed hypercharge levels are constrained within specific ranges for each orbifold.

The models are consistent with LEP experimental data within certain parameter ranges.

Abstract

We examine whether a minimal string model possessing the same massless spectra as the MSSM can be obtained from $Z_4$, $Z_6$ and $Z_8$ orbifold constructions. Using an anomaly cancellation condition of the target space duality symmetry, we derive allowable values of a level $k_1$ of U(1)$_Y$ for the minimal string model on the orbifolds through computer analyses. We investigate threshold corrections of the gauge coupling constants of SU(3), SU(2) and U(1)$_Y$ and examine consistencies of the model with the LEP experiments. It is found that $Z_4$ and $Z_8$-II can not derive the minimal string model but $Z_6$-I, $Z_6$-II and $Z_8$-I are possible to derive it with $13/12 \leq k_1\leq 41/30$, $16/15\leq k_1\leq 17/12$ and $1\leq k_1\leq 41/21$ respectively. The minimum values of the moduli on unrotated planes are estimated within the ranges of the levels.