Branes and Supergroups

Extending previous work that involved D3-branes ending on a fivebrane with θYM≠0, we consider a similar two-sided problem. This construction, in case the fivebrane is of NS type, is associated to the three-dimensional Chern–Simons theory of a supergroup U(m|n) or OSp(m|2n) rather than an ordinary Lie group as in the one-sided case. By S-duality, we deduce a dual magnetic description of the supergroup Chern–Simons theory; a slightly different duality, in the orthosymplectic case, leads to a strong-weak coupling duality between certain supergroup Chern–Simons theories on R3; and a further T-duality leads to a version of Khovanov homology for supergroups. Some cases of these statements are known in the literature. We analyze how these dualities act on line and surface operators.