Probabilistic Construction of Noncompactified Imaginary Liouville Field Theory

We propose a probabilistic construction of imaginary Liouville field theory based on a real (noncompactified) Gaussian free field. We argue that our theory represents the first explicit Lagrangian field theory that generates the imaginary Dorn, Otto, Zamolodchikov, and Zamolodchikov (DOZZ) constants without requiring a neutrality constraint. The validity of our theory is backed up by exact results on the behavior of the imaginary multiplicative chaos on a circle, and by numerical simulations on the theory on the sphere. In particular, the three point functions of the theory that are in a very good agreement with the imaginary DOZZ constant.