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

A bstract 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 theories 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 ≤ N − 2).