$Z_7$ Orbifold Models in M-Theory

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.

arXiv comment23 pages, 2 figures, 4 tables; LaTeX 3 times

References in corpus (11)

• String Theory Dynamics In Various Dimensions
• Heterotic and Type I String Dynamics from Eleven Dimensions
• The eleven-dimensional supermembrane revisited
• "Anomalous" U(1) Symmetry in Orbifold String Models
• Intersecting Orbifold Planes and Local Anomaly Cancellation in M-Theory
• On the Duality between Perturbative Heterotic Orbifolds and M-Theory on T^4/Z_N
• Dynkin diagram strategy for orbifolding with Wilson lines
• Local Anomaly Cancellation, M-Theory Orbifolds and Phase-Transitions
• An M-Theory Perspective on Heterotic K3 Orbifold Compactifications
• Intersecting Branes in M-Theory and Chiral Matter in Four Dimensions
• A "Periodic Table" for Supersymmetric M-Theory Compactifications