Free Field Realization of D-brane in Group Manifold

TL;DR

This paper constructs and analyzes the boundary state for a D-brane in the SU(2) group manifold using free field realization, matching conditions, and BRST cohomology, confirming its consistency with Cardy's state.

Contribution

It provides a direct construction of the D-brane boundary state in the SU(2) WZW model using free field techniques and matches it with Cardy's state, including BRST invariance.

Findings

Boundary state matches Cardy's state.

Boundary conditions incorporate zero modes and Weyl invariance.

Method applies free field realization to D-brane boundary states.

Abstract

We construct the boundary state for the D-brane in the SU(2) group manifold directly in terms of the group variables. We propose a matching condition for the left- and the right-moving sectors including the zero modes that describes a D-brane of the Neumann-type. The free field realization of the WZW model is used to obtain the boundary state subject to the matching condition. We show that the resulting state coincides with Cardy's state. The structure of the BRST cohomology is realized by imposing the invariance of the state under the Weyl group of the current algebra.