$Z_7$ Orbifold Models in M-Theory

TL;DR

This paper explores $Z_7$ orbifold compactifications of M-theory that can produce Standard Model-like physics, analyzing gauge symmetry breaking, matter spectra, and non-local states, with methods applicable to higher order orbifolds.

Contribution

It introduces a systematic approach to model building in M-theory using $Z_7$ orbifolds, including spectrum calculations and gauge symmetry analysis, extending previous heterotic string methods.

Findings

Identified gauge symmetry breaking patterns compatible with the Standard Model.

Calculated matter spectra including anomalous U(1) factors satisfying Green-Schwarz relations.

Presented a Dynkin diagram technique for constructing specific gauge models.

Abstract

Among $T^7/\Gamma$ orbifold compactifications of $M$-theory, we examine models containing the particle physics Standard Model in four-dimensional spacetimes, which appear as fixed subspaces of the ten-dimensional spacetimes at each end of the interval, $I^1\simeq S^1/Z_2$, spanning the $11^\text{th}$ dimension. Using the $Z_7$ projection to break the $E_8$ gauge symmetry in each of the four-planes and a limiting relation to corresponding heterotic string compactifications, we discuss the restrictions on the possible resulting gauge field and matter spectra. In particular, some of the states are non-local: they connect two four-dimensional Worlds across the $11^\text{th}$ dimension. We illustrate our programmable calculations of the matter field spectrum, including the anomalous U(1) factor which satisfies a universal Green-Schwarz relation, discuss a Dynkin diagram technique to showcase a model with $SU(3)\times SU(2)\times U(1)^5$ gauge symmetry, and discuss generalizations to higher order orbifolds.