论文标题
Liouville共形场理论的高级BPZ方程
Higher order BPZ equations for Liouville conformal field theory
论文作者
论文摘要
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 $γ\in (0,2)$.该方法包括在退化插入上重新组合奇异性，并将证明转化为代数问题。使用此方法，我们表明BPZ方程在[\ sqrt {2}，2）$ in Case $ $（R，1）$中的参数$γ\ in Sphere上保留，在情况$（r，1）$中，$γ\ in（0,2）$ in Case $（1，1，r）$。当散装宇宙常数$μ_ {\ text {bulk}} = 0 $时，相同的技术适用于边界liouville田间理论，在此，我们证明了$（r，1）$和$（1，r）$的bpz方程的$（0,2）$。
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 $γ\in (0,2)$. 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 $γ\in [\sqrt{2},2)$ in the case $(r,1)$ and for $γ\in (0,2)$ in the case $(1,r)$. The same technique applies to the boundary Liouville field theory when the bulk cosmological constant $μ_{\text{bulk}} = 0$, where we prove BPZ equations of order $(r,1)$ and $(1,r)$ for $γ\in (0,2)$.
