Probabilistic construction of non compactified imaginary Liouville field theory

2025/05/14 by Romain Usciati, Colin Guillarmou, Usciati, Romain +5 · 4 citations
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.2505.09390

openalex publication_date 2025/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

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.

Cited by

• Fourier dimension of imaginary Gaussian multiplicative chaos
• Quantum Liouville Cosmology
• On the Virasoro Crossing Kernels at Rational Central Charge
• Liouville quantum gravity: from random planar maps to conformal field theory

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