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October 16, 2025Open Access

Liouville CFT, Matrix Models and constrained WZW

Key Points

Matrix models enable realizations of Liouville conformal blocks, incorporating degeneracies and irregular operators.
Corresponding matrix integrals arise from $SL(2,ℂ)$ WZW models, under conformal constraints that lead to Liouville theory.
The study illustrates how conformal blocks connect to irregular forms of Knizhnik-Zamolodchikov equations, enhancing understanding.
Findings deepen insights into the relationship between matrix models and Liouville CFT dynamics, potentially impacting future research.

Abstract

In this paper we study matrix model realizations of Liouville conformal blocks with degenerate and irregular operators. The corresponding matrix model is Hermitian with a β-deformed measure and the degree of the potential corresponds to the degree of the irregular operator in the CFT conformal block. We then show how such matrix integrals can be obtained from an SL (2, C) WZW model with a conformal constraint giving rise to Liouville theory. The corresponding conformal blocks satisfy irregular versions of Knizhnik-Zamolodchikov (KZ) equations and we provide a matrix model realization in terms of generalized resolvents.

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Cite This Study

Babak Haghighat (Sat,) studied this question.

synapsesocial.com/papers/68f12bfb2107091eab27a3a6 https://doi.org/https://doi.org/10.48550/arxiv.2508.06901