Wilson operator algebras and ground states of coupled BF theories

Apoorv Tiwari, Xiao Chen, Shinsei Ryu

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


The multiflavor BF theories in (3+1) dimensions with cubic or quartic coupling are the simplest topological quantum field theories that can describe fractional braiding statistics between looplike topological excitations (three-loop or four-loop braiding statistics). In this paper, by canonically quantizing these theories, we study the algebra of Wilson loop and Wilson surface operators, and multiplets of ground states on the three-torus. In particular, by quantizing these coupled BF theories on the three-torus, we explicitly calculate the S and T matrices, which encode fractional braiding statistics and the topological spin of looplike excitations, respectively. In the coupled BF theories with cubic and quartic coupling, the Hopf link and Borromean ring of loop excitations, together with pointlike excitations, form composite particles.

Original languageEnglish (US)
Article number245124
JournalPhysical Review B
Issue number24
StatePublished - Jun 20 2017
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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