Probabilistic construction of non compactified imaginary Liouville field theory

TL;DR

This paper introduces a probabilistic approach to constructing imaginary Liouville Field Theory using Gaussian Free Fields, successfully reproducing structure constants without neutrality constraints, supported by exact results and simulations.

Contribution

It presents the first explicit Lagrangian field theory for imaginary Liouville that matches the DOZZ structure constants without neutrality constraints.

Findings

Three-point functions agree with imaginary DOZZ constants

Exact results for imaginary Gaussian Multiplicative Chaos obtained

Numerical simulations confirm theoretical predictions

Abstract

We propose a probabilistic construction of imaginary Liouville Field Theory based on a real (non-compactified) Gaussian Free Field. We argue that our theory is the first explicit Lagrangian field theory that reproduces the imaginary DOZZ structure constants without requiring a neutrality constraint. Our proposal is supported by exact results for the imaginary Gaussian Multiplicative Chaos on the circle, and by numerical simulations on the sphere. In particular, we show that the three-point functions of the theory agree remarkably well with the imaginary DOZZ structure constants.