Lattice construction of duality with non-Abelian gauge fields in 2+1D

Chao Ming Jian, Zhen Bi, Yi Zhuang You

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


The lattice construction of Euclidean path integrals has been a successful approach of deriving 2+1D field theory dualities with a U(1) gauge field. In this work, we generalize this lattice construction to dualities with non-Abelian gauge fields. We construct the Euclidean space-time lattice path integral for a theory with strongly interacting SO(3) vector bosons and Majorana fermions coupled to an SO(3) gauge field and derive an exact duality between this theory and the theory of a free Majorana fermion on the space-time lattice. We argue that this lattice duality implies the desired infrared duality between the field theory with an SO(3) vector critical boson coupled to an SO(3)1 Chern-Simons gauge theory, and a free massless Majorana fermion in 2+1D. We also generalize the lattice construction of dualities to models with O(3) gauge fields.

Original languageEnglish (US)
Article number075109
JournalPhysical Review B
Issue number7
StatePublished - Aug 5 2019

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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