Level-Rank Duality in Chern-Simons Theory from a Non-Supersymmetric Brane Configuration

TL;DR

This paper derives level-rank duality in pure Chern-Simons theories using a non-supersymmetric brane setup in string theory, connecting gauge theory dualities with brane configurations.

Contribution

It introduces a non-supersymmetric brane configuration approach to derive level-rank dualities in Chern-Simons theories, extending previous supersymmetric methods.

Findings

Derived level-rank duality for Sp(2N) and unitary gauge groups.

Connected IR fixed points of different Chern-Simons theories.

Established a string theory realization of non-supersymmetric dualities.

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.