Abstract
The classical Green-Schwarz superstring action, with $\mathcal{N}=1$ or $\mathcal{N}=2$ spacetime supersymmetry, exists for spacetime dimensions $D=3$, 4, 6, 10, but quantization in the light-cone gauge breaks Lorentz invariance unless either $D=10$, which leads to critical superstring theory, or $D=3$. We give details of results presented previously for the bosonic and $\mathcal{N}=1$ closed 3D (super)strings and extend them to the $\mathcal{N}=2$ 3D superstring. In all cases, the spectrum is parity-invariant and contains anyons of irrational spin.
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