Strong-Weak Chern-Simons-Matter Dualities from a Lattice Construction

TL;DR

This paper provides a lattice-based proof of dualities in (2+1)-dimensional field theories, connecting fermionic theories to bosonic Chern-Simons-matter theories, and uncovers new dualities explaining phase structures.

Contribution

It proves recent conjectures relating $U(N)$ and $SO(N)$ theories with scalars to fermions, and introduces new dualities for $SO(N)$ theories with $N-1$ and $N$ scalars.

Findings

Validated dualities between $U(N)$ level-1 theories and Dirac fermions.

Validated dualities between $SO(N)$ theories with real scalars and Majorana fermions.

Discovered new dualities explaining phase structures of $SO(N)$ theories with $N-1$ and $N$ scalars.

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 $N_f$ gauged complex Wilson-Fisher scalars (where $1\le N_f\le N$) is dual to $N_f$ Dirac fermions, as well as the analogous conjecture relating $SO(N)$ theories with real Wilson-Fisher scalars to Majorana fermions for $1\le N_f\le N-2$. 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 $N\ge 2$.