Strong-weak Chern-Simons-matter dualities from a lattice construction

Abstract

We provide a lattice demonstration of (2+1)-dimensional field theory dualities relating free Dirac or Majorana fermions to strongly-interacting bosonic Chern-Simons-matter theories. Specifically, we prove the recent conjecture that U(N) level-1 with Nf gauged complex Wilson-Fisher scalars (where 1 ≤ Nf ≤ N) is dual to Nf Dirac fermions, as well as the analogous conjecture relating SO(N) theories with real Wilson-Fisher scalars to Majorana fermions for 1 ≤ Nf ≤ N − 2. Furthermore, we discover new dualities that allow us to explain the interesting phase structure of the SO(N) theories with N − 1 and N scalars, for all N ≥ 2.