Title: Conformal Bootstrap in Liouville theory
Speaker: Remi Rhodes, Université Aix-Marseille
Time: 16:00-17:00, July9
Location: Zoom Meeting, Zoom Meeting ID: 915 8988 2960, Password: 693270
Abstract: Liouville conformal field theory (denoted LCFT) is a 2-dimensional conformal field theory studied since the eighties in theoretical physics. In the case of the theory on the Riemann sphere, physicists proposed closed formulae for the n-point correlation functions using symmetries and representation theory, called the DOZZ formula (when n=3) and the conformal bootstrap (for n>3). A probabilistic construction of LCFT was recently proposed by David-Kupiainen-Rhodes-Vargas and the last three authors later proved the DOZZ formula. In this talk I will present a proof of equivalence between the probabilistic and the bootstrap construction (proposed in physics) for the n point correlation functions with n greater or equal to 4. Basically, our proof relies on the harmonic analysis of the conformal group in two dimensions: it combines the analysis of a natural semi-group (given by the action of dilations on LCFT), tools from scattering theory and the use of Virasoro algebra in the context of the probabilistic approach (the so-called conformal Ward identities).Based on joint work with C. Guillarmou, A. Kupiainen and V. Vargas.
Video Link：https://www.bilibili.com/video/BV1PK4y1x76Q
