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.