Effective Action for D-branes on SU(2)/U(1) Gauged WZW Model

TL;DR

This paper derives the effective action for D-branes in the $SU(2)/U(1)$ gauged WZW model, including finite level corrections consistent with deformation quantization, advancing understanding of D-brane dynamics in curved backgrounds.

Contribution

It presents the first derivation of the effective action for D-branes on the $SU(2)/U(1)$ gauged WZW model, incorporating finite $k$ corrections.

Findings

Effective action derived for infinite $k$

Finite $k$ corrections compatible with Fedosov's deformation quantization

Enhanced understanding of D-brane dynamics in gauged WZW models

Abstract

Dynamics of D-branes on $SU(2)/U(1)$ gauged WZW model are investigated. We find the effective action for infinite $k$, where $k$ is the level of WZW model. We also consider finite $k$ correction to the effective action which is compatible with Fedosov's deformation quantization of the background.