Loop models, modular invariance, and three-dimensional bosonization

Hart Goldman, Eduardo Fradkin

Research output: Contribution to journalArticlepeer-review


We consider a family of quantum loop models in 2+1 spacetime dimensions with marginally long-ranged and statistical interactions mediated by a U(1) gauge field, both purely in 2+1 dimensions and on a surface in a (3+1)-dimensional bulk system. In the absence of fractional spin, these theories have been shown to be self-dual under particle-vortex duality and shifts of the statistical angle of the loops by 2π, which form a subgroup of the modular group, PSL(2,Z). We show that careful consideration of fractional spin in these theories completely breaks their statistical periodicity and describe how this occurs, resolving a disagreement with the conformal field theories they appear to approach at criticality. We show explicitly that incorporation of fractional spin leads to loop model dualities which parallel the recent web of (2+1)-dimensional field theory dualities, providing a nontrivial check on its validity.

Original languageEnglish (US)
Article number195112
JournalPhysical Review B
Issue number19
StatePublished - May 8 2018

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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