Quantum 3D Superstrings

TL;DR

This paper extends the study of 3D superstring theories to N=2 supersymmetry, revealing a spectrum of parity-invariant anyons with irrational spin, and discusses quantization constraints in various spacetime dimensions.

Contribution

It provides detailed analysis of N=2 3D superstring quantization and spectrum, building on previous work for bosonic and N=1 superstrings, and explores the implications for Lorentz invariance and particle properties.

Findings

Spectrum contains parity-invariant anyons with irrational spin

Quantization in light-cone gauge breaks Lorentz invariance unless D=10 or D=3

Extended results from N=1 to N=2 superstrings in 3D

Abstract

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.