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arXiv · 2509.01949

Free-field approaches to boundary $\mathcal{W} \big[ \widehat{g} \big] (p,p') $ minimal models

Xun Liu
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Abstract

We apply the background charged bosonic free-field approach to the rational principal quantum Drinfeld-Sokolov (QDS) $\mathcal{W} \big[ \widehat{g} \big](p,p')$ minimal models with boundaries, where $g$ is a finite bosonic simple Lie algebra. Their Ishibashi states are expressed using the free bosonic Ishibashi states, by applying the Fock space resolutions. The Coulomb-gas formalism is applied to the calculations of the disk two-point correlation functions in some well-studied and lesser familiar rational QDS $\mathcal{W} \big[ \widehat{g} \big](p,p')$ minimal models. The analytical expressions can be obtained by the repeated applications of the Pochhammer contour integral expression and the Taylor expansions of Lauricella's hypergeometric functions $F_{D}^{(n)}$.

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Xun Liu. 2025-09-02. Free-field approaches to boundary $\mathcal{W} \big[ \widehat{g} \big] (p,p') $ minimal models. https://arxiv.org/abs/2509.01949

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