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

TL;DR

This paper develops a free-field method for boundary $ ext{WZW}$ models using Lauricella hypergeometric functions, enabling explicit calculation of bulk correlation functions and boundary states in rational conformal field theories.

Contribution

It introduces a free-field framework for boundary $ ext{WZW}$ models and derives explicit genus-zero correlation functions using Lauricella functions, extending previous approaches.

Findings

Explicit bulk $n$-point functions for RCFTs derived

Free-field expressions for boundary states provided

Potential for generalization to logarithmic models discussed

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.