A free field approach to boundary $\widehat{g}_{k}$ WZW models

Abstract

The Wakimoto-type free-field approach is applied to the boundary integer-level simple $\widehat{g}(k)$ Wess-Zumino-Witten (WZW) models, with a renewed motivation. With the introduction of the Lauricella hypergeometric functions $F_{D}^{(n)}$ and their analytical extensions, we could obtain all genus-zero bulk $n$-point functions explicitly, for rational conformal field theories (RCFTs) that admit a free-field approach. I present free-field expressions for $\widehat{g}(k)$ Ishibashi states, and provide simple example calculations in the simplest models. An extreme short discussion on potential generalizations of free-field approach to the logarithmic WZW models at the admissible levels is also given.