Classification of Conformality Models Based on Nonabelian Orbifolds

TL;DR

This paper systematically analyzes nonabelian orbifold compactifications of IIB superstring theory, identifying a unique non-supersymmetric model with three chiral families based on the group D4×Z3, due to scalar sector constraints.

Contribution

It provides a comprehensive classification of nonabelian orbifolds up to order 31, discovering the only viable non-supersymmetric Standard Model-like configuration.

Findings

45 nonabelian groups considered

Most groups cannot produce chiral fermions

Only D4×Z3 yields the Standard Model with three families

Abstract

A systematic analysis is presented of compactifications of the IIB superstring on $AdS_5 \times S^5/\Gamma$ where $\Gamma$ is a non-abelian discrete group. Every possible $\Gamma$ with order $g \leq 31$ is considered. There exist 45 such groups but a majority cannot yield chiral fermions due to a certain theorem that is proved. The lowest order to embrace the nonSUSY standard $SU(3) \times SU(2) \times U(1)$ model with three chiral families is $\Gamma = D_4 \times Z_3$, with $g=24$; this is the only successful model found in the search. The consequent uniqueness of the successful model arises primarily from the scalar sector, prescribed by the construction, being sufficient to allow the correct symmetry breakdown.