A "Periodic Table" for Supersymmetric M-Theory Compactifications

TL;DR

This paper introduces a systematic classification scheme for supersymmetric orbifold compactifications of M-theory, creating a 'periodic table' organized by orbifold group order and dimension, revealing links to G2-structures.

Contribution

It presents a novel, organized classification framework for supersymmetric M-theory orbifolds, focusing on abelian cases without coordinate shifts, and explores their connection to G2-structures.

Findings

Constructed a 'periodic table' of orbifold compactifications

Organized classifications by group order and dimension

Identified links between orbifolds and G2-structures

Abstract

We develop a systematic method for classifying supersymmetric orbifold compactifications of M-theory. By restricting our attention to abelian orbifolds with low order, in the special cases where elements do not include coordinate shifts, we construct a "periodic table" of such compactifications, organized according to the orbifolding group (order up to 12) and dimension (up to 7). An intriguing connection between supersymmetric orbifolds and G2-structures is explored.