Weaving Worldsheet Supermultiplets from the Worldlines Within

TL;DR

This paper extends the classification of worldline supermultiplets to worldsheet supersymmetry, introduces new error-correcting codes for classification, and explores graphical representations of supermultiplets with complex structures.

Contribution

It develops a method to construct and classify off-shell supermultiplets of worldsheet supersymmetry using novel error-correcting codes and graphical techniques.

Findings

Classified new error-correcting codes for p+q ≤ 8.

Constructed supermultiplets without central extension.

Identified graphical representations with twisted reflection symmetry.

Abstract

Using the fact that every worldsheet is ruled by two (light-cone) copies of worldlines, the recent classification of off-shell supermultiplets of N-extended worldline supersymmetry is extended to construct standard off-shell and also unidextrous (on the half-shell) supermultiplets of worldsheet (p,q)-supersymmetry with no central extension. In the process, a new class of error-correcting (even-split doubly-even linear block) codes is introduced and classified for $p+q \leq 8$, providing a graphical method for classification of such codes and supermultiplets. This also classifies quotients by such codes, of which many are not tensor products of worldline factors. Also, supermultiplets that admit a complex structure are found to be depictable by graphs that have a hallmark twisted reflection symmetry.