Chern-Simons-matter dualities with $SO$ and $USp$ gauge groups

TL;DR

This paper extends known dualities in Chern-Simons-matter theories from unitary groups to orthogonal and symplectic groups, proposing new dualities and boundary states relevant to topological phases.

Contribution

It introduces conjectured dualities involving $SO$ and $USp$ gauge groups, generalizing previous unitary group dualities, and explores their implications for topological insulators and superconductors.

Findings

Proposed dualities between $SO(N)_k$ theories with scalars and $SO(k)_{-N+N_f/2}$ with fermions.

Clarified the form of level-rank dualities for pure Chern-Simons theories.

Identified new gapped boundary states for topological phases.

Abstract

In the last few years several dualities were found between the low-energy behaviors of Chern-Simons-matter theories with unitary gauge groups coupled to scalars, and similar theories coupled to fermions. In this paper we generalize those dualities to orthogonal and symplectic gauge groups. In particular, we conjecture dualities between $SO(N)_k$ Chern-Simons theories coupled to $N_f$ real scalars in the fundamental representation, and $SO(k)_{-N+N_f/2}$ coupled to $N_f$ real (Majorana) fermions in the fundamental. For $N_f=0$ these are just level-rank dualities of pure Chern-Simons theories, whose precise form we clarify. They lead us to propose new gapped boundary states of topological insulators and superconductors. For $k=1$ we get an interesting low-energy duality between $N_f$ free Majorana fermions and an $SO(N)_1$ Chern-Simons theory coupled to $N_f$ scalar fields (with $N_f \leq N-2$).