Weaving Worldsheet Supermultiplets from the Worldlines Within

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.Comment: Extended version, with added discussion of complex and quaternionic tensor products demonstrating that certain quotient supermultiplets do not factorize over any ground fiel

A Fermionic Hodge Star Operator

A fermionic analogue of the Hodge star operation is shown to have an explicit operator representation in models with fermions, in spacetimes of any dimension. This operator realizes a conjugation (pairing) not used explicitly in field-theory, and induces a metric in the space of wave-function(al)s just as in exterior calculus. If made real (Hermitian), this induced metric turns out to be identical to the standard one constructed using Hermitian conjugation; the utility of the induced complex bilinear form remains unclear.Comment: 11 pages, plain TeX + harvma

Golden Ratio Controlled Chaos in Supersymmetric Dynamics

We construct supersymmetric Lagrangians for the recently constructed off-shell worldline N=3 supermultiplet $Y_I/(i D_I X)$ for I=1,2,3, where $Y_I$ and $X$ are standard, Salam-Strathdee superfields: $Y_I$ fermionic and $X$ bosonic. Already the Lagrangian bilinear in component fields exhibits a total of thirteen free parameters, seven of which specify Zeeman-like coupling to external (magnetic) fluxes. All but special subsets of this parameter space describe aperiodic oscillatory response, some of which are controlled by the "golden ratio," $\varphi\approx1.61803$. We also show that all of these Lagrangians admit an $N=3\to 4$ supersymmetry extension, while a subset admits two inequivalent such extensions

Spacetime Variable Superstring Vacua

In a general superstring vacuum configuration, the `internal' space (sector) varies in spacetime. When this variation is non-trivial only in two space-like dimensions, the vacuum contains static cosmic strings with finite energy per unit length and which is, up to interactions with matter, an easily computed topological invariant. The total spacetime is smooth although the `internal' space is singular at the center of each cosmic string. In a similar analysis of the Wick-rotated Euclidean model, these cosmic strings acquire expected self-interactions. Also, a possibility emerges to define a global time in order to rotate back to the Lorentzian case.Comment: 24 pages, harvmac, HUPAPP-93/