Duality in supersymmetric Chern-Simons matter theories

Chern-Simons theories in three dimensions have many attractive features. When coupled to matter which transform under the fundamental representation of U(N), these theories are exactly solvable in the large N limit. Recently it has been conjectured that U(N) Chern-Simons theories coupled to fundamental bosons at level k is dual to U(|k|-N) Chern-Simons theories coupled to fundamental fermions at level -k. This has been explicitly verified by showing that the 2 →2 S matrices of the two theories map to each other under the duality map. We compute the 2 → 1 S matrices of supersymmetric Chern-Simons theory in a manifestly supersymmetric formalism. In the large N limit we exactly solve for the offshell four point function and obtain the S matrix by taking the onshell limit. We show that the S matrices for boson-boson and fermion-fermion map to each other under duality.