2023/02/13 by Yichao Huang, Huang, Yichao · 1 citation
Mathematics · #30F10 #60D05 #81T20 #81T40 #Boundary (topology) #Conformal field theory #Conformal map #FOS: Mathematics #FOS: Physical sciences #Gaussian #Geometry and complex manifolds #Gravitational singularity #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Mathematical analysis #Mathematics #Metric (unit) #Moment (physics) #Multiplicative function #Physics #Probability (math.PR) #Quantum mechanics #Singularity #Stochastic processes and statistical mechanics #Unit circle #Upper and lower bounds
paper · pdf · doi:10.48550/arxiv.2302.06097
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2023/02/13 · openalex created_date 2023/02/16 · openalex updated_date 2026/07/28
We determine the exact threshold of the extended Seiberg bound for the existence of correlation functions in the boundary Liouville conformal field theory in the unit disk. In probabilistic terms, our result is a toolbox yielding the threshold for the existence of positive moments of Gaussian multiplicative chaos measure, appliable to the case where singularities of arbitrary (co-)dimension in the background metric are present. We improve previous results of this type for 0-dimensional singularities in [DKRV16] and a sufficient condition for the 1-dimensional singularity in an unpublished appendix of [HRV18]. In particular, we prove the optimality of the moment bound threshold for boundary Gaussian multiplicative chaos conjectured in [HRV18], which is equivalent to the so-called unit volume Seiberg bound of the boundary Liouville conformal field theory.