Topological Spin-Statistics Theorem for Strings

Abstract

Recently, a topological proof of the spin-statistics Theorem has been proposed for a system of point particles which does not require relativity or field theory, but assumes the existence of antiparticles. We extend this proof to a system of string loops in three space dimensions and show that by assuming the existence of antistring loops, one can prove a spin-statistics theorem for these string loops. According to this theorem, all unparametrized strings(such as flux tubes in superconductors and cosmic strings ) should be quantized as bosons. Also, as in the point particle case, we find that the theorem excludes nonabelian statistics.