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Probabilistic Construction of Noncompactified Imaginary Liouville Field Theory

Romain Usciati1, Colin Guillarmou2, Remi Rhodes3, and Raoul Santachiara1

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Phys. Rev. Lett. 136, 031601 – Published 21 January, 2026

DOI: https://doi.org/10.1103/d723-gk4m

Abstract

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.

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Phys. Rev. Lett. 136, 031601– Published 21 January, 2026
  • Received 3 June 2025
  • Accepted 22 December 2025
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