Weaving worldsheet supermultiplets from the worldlines within

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 $p + q \leqslant 8$, 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.