A probabilistic approach of Liouville field theory

Abstract

In this article, we present the Liouville field theory, which was introduced in the eighties in physics by Polyakov as a model for fluctuating metrics in 2D quantum gravity, and outline recent mathematical progress in its study. In particular, we explain the probabilistic construction of this theory carried out by David–Kupiainen–Rhodes–Vargas in [] and how this construction connects to the modern and general approach of Conformal Field Theories in physics, called conformal bootstrap and based on representation theory.

Keywords

• $2D$ quantum gravity
• path integral
• Liouville field theory
• conformal bootstrap