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Quantum 3D Superstrings

The classical Green-Schwarz superstring action, with N=1 or 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 N=1 closed 3D (super)strings and extend them to the N=2 3D superstring. In all cases, the spectrum is parity-invariant and contains anyons of irrational spin.