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• W3003139484 abstract "Inspired by some intrinsic relations between Coulomb gas integrals and Gaussian multiplicative chaos, this article introduces a general mechanism to prove BPZ equations of order $(r,1)$ and $(1,r)$ in the setting of probabilistic Liouville conformal field theory, a family of conformal field theory which depends on a parameter $gamma in (0,2)$. The method consists in regrouping singularities on the degenerate insertion, and transforming the proof into an algebraic problem. With this method we show that BPZ equations hold on the sphere for the parameter $gamma in [sqrt{2},2)$ in the case $(r,1)$ and for $gamma in (0,2)$ in the case $(1,r)$. The same technique applies to the boundary Liouville field theory when the bulk cosmological constant $mu_{text{bulk}} = 0$, where we prove BPZ equations of order $(r,1)$ and $(1,r)$ for $gamma in (0,2)$." @default.
• W3003139484 created "2020-01-30" @default.
• W3003139484 creator A5001142258 @default.
• W3003139484 date "2020-02-11" @default.
• W3003139484 modified "2023-10-17" @default.
• W3003139484 title "Higher order BPZ equations for Liouville conformal field theory" @default.
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