Level-rank duality in Chern–Simons theory from a non-supersymmetric brane configuration

Abstract

We derive level-rank duality in pure Chern–Simons gauge theories from a non-supersymmetric Seiberg duality by using a non-supersymmetric brane configuration in type IIB string theory. The brane configuration consists of fivebranes, N D3 antibranes and an O3 plane. By swapping the fivebranes we derive a 3d non-supersymmetric Seiberg duality. After level shifts from loop effects, this identifies the IR of Sp(2N)2k−2N+2 and Sp(2k−2N+2)−2N pure Chern–Simons theories, which is a level-rank pair. We also derive level-rank duality in a Chern–Simons theory based on a unitary group.