Codes and Supersymmetry in One Dimension

TL;DR

This paper establishes a one-to-one correspondence between Adinkra diagrams used in supersymmetry in one dimension and doubly even codes, enabling enumeration of all possible Adinkra topologies up to N=28 and minimal supermultiplets up to N=32.

Contribution

It reveals that the topology of Adinkras is uniquely determined by doubly even codes and provides a method to enumerate these topologies systematically.

Findings

Established the correspondence between Adinkra topology and doubly even codes.

Enumerated Adinkra topologies up to N=28 and minimal supermultiplets up to N=32.

Provided a computational approach for classifying supersymmetric representations in one dimension.

Abstract

Adinkras are diagrams that describe many useful supermultiplets in D=1 dimensions. We show that the topology of the Adinkra is uniquely determined by a doubly even code. Conversely, every doubly even code produces a possible topology of an Adinkra. A computation of doubly even codes results in an enumeration of these Adinkra topologies up to N=28, and for minimal supermultiplets, up to N=32.