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

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)kChern-Simons theories coupled to Nfreal scalars in the fundamental representation, and SO(k)–N + N f / 2theories coupled to Nfreal (Majorana) fermions in the fundamental. For Nf= 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 Nffree Majorana fermions and an SO(N)1 Chern-Simons theory coupled to Nfscalar fields (with Nf≤ N − 2).