Defects in Chern-Simons theory, gauged WZW models on the brane, and level-rank duality

TL;DR

This paper explores the realization of gauged WZW models on branes within type IIB string theory, revealing how brane manipulations correspond to dualities like level-rank duality in Chern-Simons theories.

Contribution

It provides a detailed field theory construction of boundary conditions in Chern-Simons theories and connects brane dynamics to dualities in gauged WZW models.

Findings

Brane setups realize boundary gauged WZW models in string theory.

Brane moves correspond to 3d Seiberg duality and level-rank duality.

Explicit embedding of boundary theories in open string dynamics.

Abstract

We consider Hanany-Witten setups of 3- and 5-branes in type IIB string theory that realize N=(1,0),(2,0) and (1,1) gauged WZW models in 1+1 dimensions. The gauged WZW models arise as theories residing on the boundary of D3 branes ending on D5 branes. From the point of view of low energy dynamics the D5 branes play the role of half-BPS co-dimension-1 defects (domain walls) in 3d N=1 or N=2 Chern-Simons theories. Extending the analysis of previous works on the subject of boundary conditions in (supersymmetric) Chern-Simons theory, we discuss in detail the field theory construction of a large class of Chern-Simons domain wall theories and its embedding in open string dynamics. Finally, we exhibit how standard brane moves that result to 3d Seiberg duality, translate in our setup to a generalized level-rank duality in gauged-WZW models.